But the U.S. ambassador said he doubted the death of Abdulaziz al-Moqrin, who officials said was gunned down in a firefight the night before, would stop the violence against Westerners in Saudi Arabia.
Saudi officials had reported thatdumped on the northern outskirts of the capital, hours after his captors killed and decapitated him and posted Web photos of his severed head.
But officials backtracked Saturday. "We haven't found the body yet," said Adel al-Jubeir, foreign affairs adviser to Crown Prince Abdullah in Washington. "We think we know the area where it is."
Saudi security officials, speaking on condition of anonymity, said they have been searching in desert areas around Riyadh. They said they were also searching houses and apartments that they suspect were used by militants.
Al-Moqrin, who was the most wanted man in Saudi Arabia and was believed to have been behind the kidnapping, was killed along with three other militants in a gunbattle hours after Johnson's death was reported.
The other slain militants included his suspected deputy, Faisal al-Dukheil, "who is believed to be the number-two al Qaeda person in Saudi Arabia," al-Jubeir said.
Al-Moqrin is believed to have had a leading role in the stepped-up campaign of militant violence in the kingdom, which in recent months has seen bombings and gun attacks on foreigners.
"This was a major blow to al Qaeda in Saudi Arabia," al-Jubeir said. But he acknowledged that there are likely other al Qaeda cells in the kingdom seeking to topple the royal family for its close ties to the United States.
U.S. Ambassador James C. Oberwetter praised Saudi security forces for their work, including the killing of al-Moqrin. But he said the situation in the kingdom remained dangerous for Westerners.
"It will be some time before we achieve a comfort level that the situation returns to normal," Oberwetter said at a press conference in Riyadh.
"A great deal was accomplished last evening but we also believe that much more remains to be done," he said.
"The Saudis are doing an excellent job working on their most wanted list and taking people of that list," he said. "But not everyone has been removed from the list. Maybe there are more."
As many as 35,000 Americans live and work in heavily fortified compounds in Saudi Arabia, points out CBS News Correspondent Joie Chen. Many have stayed for years, and play critical roles in the kingdom's oil industry.
Saudi leaders are urging Americans not to let the latest attacks frighten them away, reports Chen. They say that would hand victory to terrorists. It could also have a significant impact on the kingdom's biggest source of income - its oil.
But Americans working in Saudi Arabia fear a new terrorist will step in to replace the alleged al Qaeda leader reportedly killed by police.
They found little comfort in the government's announcement that al-Moqrin and three other militants had died in a gunbattle Friday night after killing Johnson.
"I am worried about who is going to step up to take his place and how many of these militants are out there," Jack Smith, 49, an information technology executive in Riyadh, said Saturday.
"I hope the Saudis will squash them all soon," the St. Louis native said of the extremists who have stepped up attacks on Westerners in hopes of undermining the desert kingdom's royal family.
Johnson's family remained in seclusion Saturday. Relatives who had gathered since he was taken hostage a week earlier issued a statement Friday that was delivered by an FBI agent. In it, they asked for privacy and commended authorities in their failed attempts to save Johnson.
Saudi TV broadcast pictures Saturday of four bloodied bodies it said were al-Moqrin and the three other slain militants, apparently to refute denials by Islamic militants that al-Moqrin was dead. A posting on an Islamist Web site Saturday said claims of al-Moqrin's death were "aimed at dissuading the holy warriors and crushing their spirits."
The four were killed in an hours-long gunbattle after Saudi security forces intercepted their car in Riyadh's al-Malaz neighborhood at one of the mobile, "surprise" roadblocks they have been setting up in the capital, al-Jubeir said.
"The terrorists tried to shoot their way out," he said.
One security officer was killed and two were wounded in the gunbattle, the official Saudi Press Agency reported.
The Interior Ministry said 12 suspected militants were also arrested in a sweep of the capital during the night.
A security official in Riyadh said Rakan Mohsen Mohammed Al Saykhan, the second most-wanted Saudi militant, was wounded in the clash and was one of those arrested.
He is an alleged associate of the mastermind of the bombing of the USS Cole in Yemen's port of Aden in October 2000.
The Interior Ministry said authorities had confiscated three cars used by al-Moqrin's cell, including one believed to have been used in the June 6 killing of Irish cameraman Simon Cumbers.
Also confiscated were forged identity papers, $38,000 and a weapons cache, including three rocket-propelled grenade launchers, hand grenades and automatic rifles, the statement said.
The Saudi Press Agency identified the other killed militants as Turki bin Fuheid al-Muteiry and Ibrahim bin Abdullah al-Dreiham.
Al-Dikheel may have appeared in video footage of Johnson's killing, the SPA report said.
Al-Muteiry was among the militants who was involved in the May 29 shooting and hostage-taking, it said. Al-Dreiham was linked to the Nov. 8, 2003, suicide bombing at , the statement added.
Crown Prince Abdullah, the de facto ruler, and other top officials have said the crackdown is the beginning of the end of terrorism in the kingdom that has killed scores of people and scared some foreigners away from the oil-rich nation.
"We have substantially weakened the organization. ... We will continue to pursue them with vigor until we eliminate them from our midst," al-Jubeir said.
Saudi analysts have estimated that there are some 2,000 militants in the kingdom who might have links with Osama bin Laden's al Qaeda terror network or its sympathizers.
Dia'a Rashwan, a Cairo expert on Islamic militants, said the death of al-Moqrin will not end terrorism in Saudi Arabia, where he said conservative Islamic traditions makes it fertile ground for extremism.
"There are always new generations who can take over and continue their course," he said.
Al-Moqrin took over al Qaeda operations in the kingdom after his predecessor, Khaled Ali Haj, was killed by security agents earlier this year, but he had masterminded attacks before that. Haj succeeded Youssef al-Airi, who was killed in a clash with Saudi security forces in early 2003.
Rashwan said, however, that the replacement terrorists may lack the combat skills and expertise of their predecessors, who, like al-Moqrin, trained in Afghanistan and elsewhere.
Al-Moqrin, known as a smart and brutal tactician, was the most-wanted militant in Saudi Arabia. His attacks in recent months have shown tactical flexibility - devastating car bombs as well as pinpointed strikes like the kidnapping of Johnson, a first in the kingdom.
Johnson, 49, was kidnapped last weekend by militants who threatened to kill him by Friday if the kingdom did not release its al Qaeda prisoners. The Saudi government rejected the demands.
Three photos of Johnson's body, the head severed, were posted on the Internet when the deadline ran out. A statement said "the infidel got his fair treatment. ...Let him taste something of what Muslims have long tasted from Apache helicopter fire and missiles."
It was issued in the name of the Fallujah Brigade of al Qaeda in the Arabian Peninsula.
Johnson had worked on Apache helicopters for Lockheed Martin.
Johnson was seized on June 12, the same day that Islamicof Laconia, New Hampshire, in his garage in Riyadh.
Scroggs worked for Advanced Electronics Co., a Saudi firm whose Web site lists Lockheed Martin among its customers. The office number on Johnson's business card was for Advanced Electronics.
The same week as Scroggs' death, militants shot and killed another American, Robert Jacobs, and Cumbers in Riyadh.
World governments condemned Johnson's beheading.
President Bush condemned the beheading and vowed that "America will not be intimidated by these kinds of extremist thugs." British Prime Minister Tony Blair called the killing "an act of barbarism." Condemnation also came from Arab governments and Islamic leaders in Indonesia, the world's largest Muslim nation.
Ahmad Haj Ali, a Syrian Information Ministry official, called Johnson's killing "a shameful crime, which is alien to Arab and Muslim morals."
But one Islamic leader in Indonesia predicted more killings of the kind unless the United States changes its approach toward the Middle East.
Irfan Awwas, chairman of the Majelis Mujahidin Indonesia, a radical Islamic group, said that to avoid more such attacks, the United States should leave Iraq and Afghanistan and stop Israeli violence against Palestinians.
"The killing of innocent people is wrong," Awwas said. "But it is a result of the United States policies in the Middle East."
Moderate Islamic leaders in Indonesia, however, said Johnson's death would do little to change U.S. policy.
"This will only create more violence and won't solve the problem. It will only strengthen the American resolve," said Azyumardi Azra, a Muslim scholar at the National Islamic University in Jakarta.
Indonesia has faced a growing threat from radical religious groups, including the al Qaeda-linked Jemaah Islamiyah. The group is blamed for the Oct. 12, 2002, bombings that killed 202 people, mostly foreign tourists, on Indonesia's Bali island.
CBS News Correspondent Sheila MacVicar reports that for Americans living in Saudi Arabia, the murder of Paul Johnson may make some reconsider their decision to stay in the country.
"I think they're going to be rattled and very frightened about what happened,'' said one American, who asked not to be identified. "The manner in which he died is extremely horrific and shocking.
In Jordan, King Abdullah II said on state-run Jordanian radio it was "scary and humiliating that this crime has been committed in the name of Islam."
French President Jacques Chirac said he was "horrified" by Johnson's killing, which he described as beastly and inhuman.
"I can only express the shame that we all feel faced with the behavior coming from human beings of this nature," Chirac said Friday at a summit of European Union leaders in Brussels.
Australian Prime Minister John Howard called the slaying an "evil act without any conceivable justification."
U.N. Secretary-General Kofi Annan said "these kinds of brutal acts do not help anybody."
"My sympathies go to his family and loved, and I hope the perpetrators would eventually be brought to justice because we cannot tolerate this kind of behavior in today's world," he said at the U.N. headquarters in New York.
In Thailand, leaders expressed sympathy for Johnson's Thai wife Thanom, who issued a tearful, televised plea to her husband's captors on the eve of his execution.
The New York-based Human Rights Watch called Johnson's slaying "a heinous crime that no political cause can justify."