The White House, in line with longstanding policy not to discuss threats on the president, declined to comment today.
In an interview on French television on Monday, President Hosni Mubarak of Egypt spoke in specific terms about the threat, saying that "on June 13 of this year, we learned of a communiqué from bin Laden saying he wanted to assassinate George W. Bush and other G8 heads of state during their summit in Italy."
"It was a well-known piece of information," Mr. Mubarak added in the interview broadcast by the network France 3.
Separately, he told Le Figaro, a major French daily newspaper, that Egyptian intelligence services had told the United States about the threat and that the warning included a reference to "an airplane stuffed with explosives."
Several days before Mr. Mubarak's interview, in an appearance on Italian television, Gianfranco Fini, the Italian deputy prime minister, discussed parallels between the attacks on the World Trade Center and the Pentagon, and warnings his government had received before the Genoa meeting in July.
"Many people joked about the Italian Intelligence Force," Mr. Fini said, "but actually they had information that in Genoa there was the hypothesis of an attack on the American president with the use of an airplane. That is why we closed the airspace above Genoa and installed antiaircraft missiles. Those who joked should now reflect."
The senior American security official said the source of warnings from foreign intelligence agencies was often unclear, and the volume was so great that serious threats were frequently difficult to separate from false alarms.
A senior administration official, who could not confirm the accounts, said that foreign intelligence agencies frequently received tips about threats to the president that they passed on to Washington.
While there was a general concern about Mr. bin Laden before the July conference in Italy, there had also been concerns about Islamic extremists at other summit meetings, including the Asian Pacific Economic Cooperation meeting in Brunei last year, attended by President Clinton.
There was no attack in Genoa. It was marked chiefly by violent protests in the streets by anarchists and anticapitalist demonstrators that resulted in many injuries and the death of one protester at the hands of the Italian police.
But participants and reporters who flew into the Christopher Columbus airport, which was closed to commercial traffic, were greeted by the unusual sight of antiaircraft batteries along the runways.
One senior American official who has been involved in a number of such summit conferences said today, "It's something I have never seen before, especially in such an obvious spot."
Since the Sept. 11 attacks in New York and Washington, European and American officials have been reviewing threats from Mr. bin Laden's organization in June and July. Those threats resulted in a number of public warnings around the July 4 holiday, and extra security precautions for Mr. Bush.
But after nothing materialized, the concern waned.
The most specific warning that Mr. bin Laden planned an attack apparently came from Egyptian intelligence sources.
In his interview with Le Figaro, published late last week, Mr. Mubarak said: "We had communicated to the Americans certain information from the video made by bin Laden on the 13th of June. It spoke of assassinating President Bush and other heads of state in Rome. It was a question of an airplane stuffed with explosives. These precautions then had been taken."
However, people who have viewed the tape say there is no reference on it to any airplane stuffed with explosives, no specific threat to kill the President, and no mention of an attack by aircraft.
President Mubarak added that "no one had imagined that Boeings filled with passengers would be crashed against the buildings."
Italian officials say that the antiaircraft batteries they set up in Genoa were primarily intended to deter an attack from a small plane.