The FBI has contacted Deborah Ramirez, a woman who accused Brett Kavanaugh of sexual misconduct when he was a Yale student, as part of its renewed investigation of the supreme court nominee.

Ramirez alleges that Kavanaugh exposed his genitals to her at a party in the early 1980s, when they were both students in New Haven, Connecticut. Her lawyer, John Clune, said in a statement on Saturday agents wanted to interview her and she had agreed to cooperate.

Donald Trump ordered the FBI to reopen its investigation after three women accused Kavanaugh of sexual misconduct and the first woman, Dr Christine Blasey Ford, testified before the Senate judiciary committee. Kavanaugh denies all the allegations.

NBC News reported on Saturday that the White House had placed constraints on the investigation including that the third woman to accuse Kavanaugh, Julie Swetnick, would not be questioned. Citing “a US official briefed on the matter”, NBC said the White House controlling such a process for a presidential nominee was not unusual.

Trump countered on Twitter, saying NBC “incorrectly reported (as usual) that I was limiting the FBI investigation of Judge Kavanaugh, and witnesses, only to certain people. Actually, I want them to interview whoever they deem appropriate, at their discretion. Please correct your reporting!”

NBC News changed the headline on its piece but stood by its reporting that Swetnick would not be questioned.

On Thursday, Kavanaugh and Ford testified in an electric session on Capitol Hill in Washington.

Ford, who says Kavanaugh and a friend attacked her at a house party in Maryland in 1982, gave her testimony first.

Kavanaugh prefaced his testimony with angry criticism of Democrats for what he said was a politically motivated attack.

On Friday, after protesters confronted the committee member Jeff Flake in an elevator in the Senate office building, the Arizona Republican requested the renewed FBI investigation. Flake nonetheless voted for the nomination to proceed to the Senate floor.

Senate leaders agreed to delay the final vote to allow for a one-week investigation. The judiciary committee said the FBI investigation should be limited to “current credible allegations” against Kavanaugh and be finished by Friday 5 October.

Swetnick came forward on Wednesday. She said she was at parties in the 1980s where Kavanaugh and his friend Mark Judge – whom Ford alleges was there when she was allegedly attacked – were present when women were gang-raped.

In a statement, she wrote: “In approximately 1982, I became the victim of one of these ‘gang’ or ‘train’ rapes where Mark Judge and Brett Kavanaugh were present.” She did not say Judge or Kavanaugh participated in the alleged rapes.

Judge strongly denied Swetnick’s allegations. He has said he has no memory of the party described by Ford. He was not called to testify to the Senate judiciary committee, which is controlled by Republicans.

Having disappeared from the public eye, Judge was found by the Washington Post in a beach house in Delaware. His lawyer said on Friday he would be willing to talk to the FBI “or any law enforcement agency”.

Swetnick is represented by Michael Avenatti, the attorney for Stormy Daniels, the adult film star and director who says she had a sexual liaison with Trump. The president denies the affair, as he does allegations of sexual misconduct from more than a dozen women.

Trump tweeted an attack on Avenatti this week, calling him a “total low-life” and “a third rate lawyer who is good at making false accusations, like he did on me and like he is now doing on Judge Brett Kavanaugh”.

On Saturday, Avenatti told the Post he did not “know how this investigation could be called complete” if the FBI did not contact his client.

Trump, meanwhile, repeated a familiar attack on a Democratic member of the Senate judiciary committee, Richard Blumenthal, over what the president called his “fraudulent service in Vietnam”.

Like Trump, Blumenthal received deferments from service as a student. Unlike Trump, he then served in the US Marine Corps without leaving the US. Before being elected in 2010, Blumenthal occasionally said he had been “in Vietnam”.

Kavanaugh’s confirmation would tilt the supreme court to the right, potentially placing in question rulings on issues including abortion rights.

Republicans hold the Senate 51-49 and would need a simple majority to confirm Kavanaugh. Two moderate Republican women – Susan Collins of Maine and Lisa Murkowski of Alaska – will be key votes if the nomination reaches the floor.

Democrats facing midterm contests in Republican-leaning states will also face pressure. On Saturday, Joe Manchin of West Virginia, was set to see his state host a Trump campaign rally.