Earlier, the al Qaeda group that kidnapped Johnson said in an online statement Friday that it had killed the hostage, and posted three still photographs of his beheaded body.
"In answer to what we promised … to kill the hostage Paul Marshall after the period is over … the infidel got his fair treatment. … Let him taste something of what Muslims have long tasted from Apache helicopter fire and missiles," the statement said.
President Bush condemned the brutal murder, saying it reveals the "evil nature" of the enemy. Mr. Bush told reporters in Seattle the kidnappers are trying to "get us to retreat from the world." But, he said, America "will not be intimidated by these kind of extremist thugs."
Vice President Dick Cheney also condemned the killers. "They have no shame, not a shred of decency, and no mercy. America will hunt down the killers, one by one, and destroy them."
In London, Prince Turki al-Faisal, the Saudi ambassador to the United Kingdom, said, "This is an evil act by evil people." He vowed, "We will continue to use every effort to fight this murderous cult in Saudi Arabia."
One of the three photographs posted on the Internet site showed a man's head, face toward the camera, being held by a hand. The other two showed a beheaded body lying prone on a bed, with the severed head placed in the small of his back.
The face looked like Johnson's.
The beheaded body was clad in a bright orange suit, similar to those issued to suspected Islamic militants imprisoned by the United States at Guantanamo Bay — and similar to the suit another American captive, Nicholas Berg, was wearing when he was beheaded in Iraq last month by another group of Islamic militants inspired by al Qaeda.
"To the Americans and whoever is their ally in the infidel and criminal world and their allies in the war against Islam, this action is punishment to them and a lesson for them to know that whoever steps foot in our country, this decisive action will be his fate," the statement said.
Soon after the statement appeared, the Web site was inaccessible with a message saying it was closed for maintenance.
Arab satellite network Al-Arabiya said there was also a video of the beheading.
Johnson was kidnapped last weekend by militants calling themselves al Qaeda in the Arabian Peninsula. They threatened to kill him by Friday if the kingdom did not release its al Qaeda prisoners.
Johnson, who had spent more than a decade in Saudi Arabia, worked on targeting and night vision systems for Apache helicopters. The group cited his job as one of the reasons he was kidnapped.
CBS News Correspondent Dan Raviv reports that until a few years ago, Saudi Arabia was a tightly-controlled country. The royal family -- the House of Sa'ud -- seemed to be closely connected with the most influential religious leaders.
But since Sept. 11, then with anger at America for invading Iraq, radical Islam seems to have gained strength in Saudi Arabia. A symptom is this upsurge in violence, Raviv reports.
Johnson's abduction was the latest in a series of terrorist attacks in Saudi Arabia, many of which have targeted Westerners.
The day Johnson was seized, Islamic militants shot and killed Kenneth Scroggs, from Laconia, N.H., in his garage. An Irish cameraman for the British Broadcasting Corp. was killed on June 6 and another American was slain in his garage June 8.
Late last month, 22 people, most of them foreigners, were killed in a shooting rampage and hostage-taking in the eastern Saudi oil hub of Khobar. On May 1, gunmen entered the office of an oil contractor in Saudi Arabia and began shooting at random, killing at least seven people, including two American engineers.
In mid-April, two car bombs blasted the Saudi national police headquarters, killing at least nine people and wounding 125 others, police said.
The recent attacks come a year after the Saudi government began a crackdown following major terrorist attacks on May 12, 2003, which also targeted and killed Westerners.
Back in the United States, Johnson's family was in seclusion Friday at a town house in New Jersey decorated with yellow ribbons.
An unidentified woman stood outside the house, weeping. A man outside the house who identified himself only as Bill said the family did not want to talk to reporters.
Earlier on Friday, appearing on Saudi TV and struggling to hold back tears, Johnson's Thai wife pleaded for kidnappers to release her husband, saying "please bring him back to me."
"When I see his picture in TV, I fall down," Thanom Johnson said. "When I hear the name Paul Johnson, I cry a lot. He is my only family here."