How the bureau is conducting the investigation — and in particular, how many witnesses will be interviewed — has been the subject of fierce debate on Capitol Hill. The White House, which has control over the scope of the investigation, initially gave the F.B.I. the names of just four witnesses. But on Monday, after a backlash from Democrats, Mr. Trump said the bureau “should interview anybody that they want within reason.”

The bureau appears to be moving quickly; on Tuesday, investigators wrapped up an interview with a crucial witness, Mark Judge, a friend and high school drinking buddy of Judge Kavanaugh who has been identified as the only witness to the alleged sexual assault of Dr. Blasey. Mr. Judge’s name came up frequently last week when the judge and Dr. Blasey testified before the Judiciary Committee.

The lawyer for another critical witness, Tim Gaudette, also confirmed that he had been interviewed by F.B.I. agents. Judge Kavanaugh’s calendar for July 1, 1982, indicates he had gone to Mr. Gaudette’s house with some of the people identified by Dr. Blasey as attending the small gathering at which she was assaulted. Democrats have asked for more details about the events of that day.

But lawyers for Dr. Blasey and another woman, Deborah Ramirez, complained independently on Tuesday that the bureau was not pursuing important leads. Dr. Blasey, who testified that Judge Kavanaugh had tried to rape her at a house party when they were teenagers, has not been interviewed, nor have other “witnesses we have identified,” her lawyers wrote in a letter Tuesday to the F.B.I. director and chief counsel.

Ms. Ramirez, who did not testify, has accused Judge Kavanaugh of exposing himself to her during a drunken dormitory party at Yale. She spent more than two hours on Sunday with F.B.I. investigators, her lawyer, John Clune, said on Twitter on Tuesday.

But while Mr. Clune wrote that “the agents were clearly motivated to investigate the matter in any way they were permitted,” he expressed doubts about whether they would pursue more than 20 additional witnesses that Ms. Ramirez identified. He said he and his client “have great concern that the FBI is not conducting — or not being permitted to conduct — a serious investigation.”