"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.
Johnson, 49, worked on targeting and night vision systems for Apache helicopters, and the group had cited his job as one of the reasons he was kidnapped.
"We, God willing, will continue our road to fight the enemies of God," the statement said.
The U.S. Embassy in Riyadh had no immediate comment. "We are working on verification," the spokesperson said.
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.
An Internet site often used by Islamic militant groups linked to al Qaeda displayed a link to Johnson's beheading, but initial efforts to access the video were unsuccessful.
Johnson was kidnapped last weekend by militants calling themselves al Qaeda in the Arabian Peninsula who threatened to kill him by Friday if the kingdom did not release its al Qaeda prisoners.
A Saudi senior security official, reached by The Associated Press, said: "We have so far nothing on this."
In Washington, a CIA spokesperson said the agency was not able to immediately confirm the report of Johnson's beheading.
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.
Security forces had intensified their search for Johnson in fundamentalist strongholds of the Saudi capital Friday as the deadline approached.
Police vehicles drove through the Sweidi, Dhahar al-Budaih and Badr districts from Thursday night through Friday morning, but the authorities gave no indication they were any closer to finding Johnson.
Later Friday, security forces expanded their searches to other suburbs of Riyadh. Police stopped cars at checkpoints throughout the capital. FBI experts in hostage negotiation were standing by, reports CBS News Correspondent Steve Holt.
A senior Saudi official in the United States directly familiar with the investigation said Thursday night that U.S. and Saudi officials have had few promising leads.
More than 15,000 Saudi officers had been deployed in the search of Riyadh, going door-to-door in some neighborhoods. More than 1,200 Saudi homes had been searched as of Thursday night.
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."
In the United States on Friday, Johnson's family was in seclusion. Police kept the media off the property outside the home of Donna Mayeux, Johnson's sister. An American flag and yellow ribbons were hung from the front porch, but there was no sign of activity inside.
Hundreds of supporters held candlelight vigils Thursday night in Johnson's New Jersey hometown and in Florida, where he lived before moving to the Middle East. Johnson, 49, had worked in Saudi Arabia for more than a decade.