Officials said Mr. Mueller, who was sworn in last month, believed that his agents had a broad understanding of the events of Sept. 11 and now needed to concentrate on intelligence suggesting that other terrorist attacks were likely. He said at a news conference last week that the bureau was trying to follow up on 260,000 tips, about half of them received on a special hot line and Internet site.

The F.B.I. has described the investigation of the terrorist hijackings as the most exhaustive in its history. Even minor witnesses say they have been interviewed repeatedly, which appears to have alarmed some officials who believe that agents should instead be chasing tips suggesting new terrorist attacks. A woman in Florida who was a neighbor to two of the hijackers said last week that she had been interviewed 18 times by the F.B.I.

At a news conference today, Mr. Ashcroft said federal, state and local law enforcement agencies were placed ''on the highest level of alert'' after the United States began a military strike on Afghanistan on Sunday.

''We are taking strong precautions and other appropriate steps to protect the American people while we win this war,'' he said, announcing that 614 people had been arrested or detained during the investigation, up from about 500 early last week.

Some officials suggest that Mr. Ashcroft has in effect taken command of F.B.I. operations along with Mr. Mueller, often spending hours a day in the 40,000-square-foot Strategic Information and Operations Center at F.B.I. headquarters on Pennsylvania Avenue, across the street from the Justice Department.

That has rankled some veteran rank-and-file agents, who regard his assertiveness as an intrusion that threatens the traditional independence of the F.B.I. within the Justice Department, its parent agency. Others at the Justice Department say they welcome the close cooperation between the department and the F.B.I. after years of discord.

''This is important progress,'' a senior official said.

Mr. Ashcroft's relationship with Mr. Mueller contrasts sharply to that of Janet Reno, the former attorney general, and Louis J. Freeh, who preceded Mr. Mueller. Mr. Freeh was assertively independent, and at times he acted in direct opposition to the wishes of Ms. Reno.