"We understand that between now and the election, there is a window of time in which terrorists may well wish to influence events, whether it's in the United States or overseas," Mueller said in an interview with The Associated Press.
He also said Islamic extremists are changing tactics to focus on recruitment of local sympathizers less likely to arouse suspicion than outsiders. And terrorist groups may well move away from fortified targets, such as airports and government buildings, he said Thursday.
"I do believe that when we enhance our security, harden targets, terrorists look for other targets that are soft targets," Mueller said. When new security measures are taken, he said, "the terrorists are thinking about ways to circumvent them."
The March 11 train bombings in Madrid that killed 190 people were a factor in the ouster of Spain's government. That has added to uneasiness about the U.S. political conventions in New York and Boston this summer.
"In the wake of what happened in Madrid, we have to be concerned about the possibility of terrorists attempting to influence elections in the United States by committing a terrorist act," Mueller said. "Quite clearly, there will be substantial preparations for each of the conventions."
U.S. officials also are very worried about security for the Athens Olympics in August. Mueller said he was awaiting a review of a recent anti-terrorism exercise to "see again what we could do if there are areas that need to be shored up."
Asked if security would be adequate by the time the Olympics begin, Mueller said: "It's premature to make any definitive judgment as to where we are in the stages of preparations."
Regarding new al Qaeda recruiting tactics, Mueller pointed to the May 16, as evidence of change. In those attacks, local Islamic extremists were recruited by outsiders probably linked to al Qaeda to carry out the mission.
"We, along with our counterparts, have to be alert to that type of combination of local persons as well as others who may have expertise in timing devices and constructing (bombs), coming together with those who are willing to sacrifice themselves," Mueller said.
He said there is no good explanation as to why no suicide bombings have been attempted in the United States - "knock on wood," he said - other than the FBI's effort to make state and local law enforcement officials aware that "this is a threat" and "the need to be alert to it."
Mueller praised the efforts of Saudi Arabia andin assisting U.S. counterterrorism efforts. Saudi Arabia in particular has moved aggressively to root out al Qaeda cells since last May's bombings in Riyadh, discovering tons of explosives and large caches of weapons.
"Saudi Arabia has become a very inhospitable place for al Qaeda," Mueller said. "That was not always the case."
He said about 70 FBI agents, analysts and other personnel helped the Saudis investigate the bombings.
In the interview, Mueller also said:
By Curt Anderson