FBI agents have interviewed one of the three women who have accused US Supreme Court nominee Brett Kavanaugh of sexual misconduct.

The White House insisted it was not “micromanaging” the new one-week review of Kavanaugh’s background but some Democrats claimed the White House was keeping investigators from interviewing certain witnesses.

President Donald Trump, for his part, tweeted that no matter how much time and discretion the FBI was given, “it will never be enough” for Democrats trying to keep Kavanaugh off the bench.

And even as the FBI explored the past allegations that have surfaced against Kavanaugh, another Yale classmate came forward to accuse the federal appellate judge of being untruthful in his testimony to the Senate Judiciary Committee about the extent of his drinking in college.

In speaking to FBI agents, Deborah Ramirez detailed her allegation that Kavanaugh exposed himself to her at a party in the early 1980s when they were students at Yale University, according to a person familiar with the matter who was not authorised to publicly discuss details of a confidential investigation.

Kavanaugh has denied Ramirez’s allegation.

Yale classmate of Kavanaugh’s said he is “deeply troubled by what has been a blatant mischaracterisation by Brett himself of his drinking at Yale.”

Charles “Chad” Ludington, who now teaches at North Carolina State University, said he was friend of Kavanaugh’s at Yale and that Kavanaugh was “a frequent drinker, and a heavy drinker”.

Speaking to the issue of the scope of the FBI’s investigation, White House press secretary Sarah Huckabee Sanders said, “The White House isn’t intervening.”

White House counsellor Kellyanne Conway said the investigation will be “limited in scope” and “will not be a fishing expedition. The FBI is not tasked to do that.”

Republicans control 51 seats in the closely divided 100-member Senate and cannot afford to lose more than one vote on confirmation.

Trump initially opposed such an investigation as allegations began mounting but relented and ordered one on Friday. He later said the FBI has “free rein”.

At least three women have accused Kavanaugh of years-ago misconduct. He denies all the claims.