BOSTON (CBS) – Arizona Sen. Jeff Flake said in Boston Monday he wants the FBI to make sure any current, credible allegation against Supreme Court nominee Brett Kavanaugh is fully investigated.

Flake gave an interview at the Forbes 30 Under 30 event at City Hall Plaza and at times had to speak over protesters’ shouts of “Vote No!”

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“We certainly want the FBI to do a real investigation,” Flake said. “We are working to make sure that that happens.”

Flake said his staff has been in contact with the White House counsel to make sure the investigation is “up to standard.”

Senator Jeff Flake speaks at the Forbes 30 Under 30 event in Boston (WBZ-TV)

“It does no good to have an investigation that just gives us more cover,” he said. “We actually need to find out what we can find out and we have to realize we may not be able to find out everything that happened.”

While the crowd waited for Flake, former Secretary of State and Massachusetts Senator John Kerry took the stage and scolded Republicans for trying to rush the FBI investigation and quickly push through Kavanaugh’s confirmation.

“There is no reason in the world to be bum-rushing this nomination when the very people who are rushing it were people who were willing to hold Merrick Garland for 14 months without a hearing, without a visit. It’s wrong,” Kerry told the crowd.

Earlier in the day, as many as 2,000 protesters, including Boston Mayor Marty Walsh, Sen. Ed Markey, congressional candidate Ayanna Pressley, New York congressional candidate Alexandria Ocasio-Cortez and Olympic figure skater Adam Rippon, gathered on the plaza just after 10 a.m. calling for Flake to reject Kavanaugh’s nomination to the Supreme Court.

“I’m glad they’re here, I’m glad people are making their voice heard,” Flake told reporters after the event. “I’ve heard very compelling stories this week and I am sure we will continue to.”

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Watch: Adam Rippon addresses crowd

In a surprise move during Friday’s Senate Judiciary Committee meeting to vote on the nomination, the Republican called for an FBI investigation into sexual assault claims against Kavanaugh before the full Senate votes on his nomination.

Arizona Sen. Jeff Flake was confronted by protesters over the Kavanaugh nomination in an elevator, Sept. 28, 2018. (Image credit: 60 Minutes)

“I just knew that we couldn’t move forward, that I couldn’t move forward without hitting the pause button because of what I was seeing and experiencing in an elevator and in committee and thinking this is ripping our country apart,” Flake told CBS’ “60 Minutes” Sunday.

A large crowd of protesters called for an end to the Supreme Court nomination of Brett Kavanaugh on City Hall Plaza in Boston Monday. (WBZ-TV)

“A lot of people are thanking him for what happened Friday, but that’s his job. His job is to ask tough questions, his jobs is to do an investigation. The whole committee’s job was to vet the candidates and they clearly didn’t do it in this case and I think there’s still a lot of work to be done,” Walsh told reporters before the rally Monday.

Flake also attended another event at St. Anselm College in Manchester, New Hampshire Monday evening. About two dozen protesters showed up to try and sway his vote.

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WBZ-TV’s Mike LaCrosse reports