Flake, whose reservations about Kavanaugh led to Trump requesting a supplemental background check on his nominee last week, also condemned the President's comments.
The FBI didn't interview Kavanaugh or Christine Blasey Ford, who testified before the Senate Judiciary Committee last week about her allegations against him. Also interviewed were two others Ford said were present but in a different room: Patrick "P.J".
In particular, Democrats have homed in on his contention that the allegations against him are an "orchestrated political hit" funded by left-wing groups seeking "revenge on behalf of the Clintons".
There is debate on Capitol Hill as to whether all or some of the report should be made public.
Addressing a campaign rally in MS on Tuesday night, Trump cast doubt on Ford's allegation that Kavanaugh, his nominee for the USA supreme court, attempted to rape her when the two were teenagers in the early 1980s. However, Ford's counsel has criticized the investigation for not interviewing her nor Kavanaugh in the process. With Republicans holding a thin 51-49 majority and five senators, including three Republicans, not committed to approving Kavanaugh, the conservative jurist's prospects of Senate confirmation remained murky.
Trump ordered the FBI to reopen the investigation into Kavanaugh last week after a dramatic last-minute demand by Senator Flake during the Senate Judiciary Committee's vote on the nominee.More news: Federal government and Ontario spar over USMCA trade deal
Also Wednesday, the National Council of Churches, a coalition of 38 denominations, released a statement saying Kavanaugh should withdraw his nomination.
The bureau's investigation, ordered last week by President Trump, was created to look into allegations of sexual misconduct leveled at Kavanaugh, who has been accused by three women of separate alleged incidents.
He pledged that the full U.S. senate would begin voting on Mr Kavanaugh's nomination this week. Their letter said, he "displayed a lack of judicial temperament that would be disqualifying for any court, and certainly for election to the highest court of the land".
One of them is Republican Jeff Flake of Arizona, who was greeted by hundreds of liberal protesters, victims of sexual assault among them, during an appearance on Monday in Boston.
President Donald Trump is pictured gesturing as he speaks during a rally in Southaven, Mississippi.
FILE - In this February 15, 2018, photo, Sen.More news: Atletico visit Real in key Madrid derby on Saturday
Alaska Senator Lisa Murkowski called the remarks "wholly inappropriate and in my view unacceptable". Susan Collins (R-Maine) and Sen.
Those GOP senators, along with Democrats Heidi Heitkamp of North Dakota and Joe Manchin of West Virginia, have yet to declare how they will vote on Kavanaugh.
On Friday, he voted to move the nominee out of committee but called for an FBI investigation into allegations made against Kavanaugh in order to gain more clarity on the matter before the full Senate votes on his nomination.
"I had one beer!" he said, impersonating Ford. I don't care how many members they chase, how many people they harass here in the halls, we will not be intimated by these people, how many people they harass here in the halls. "That's the only thing I remember".
"The issues of credibility and temperament are not something that happened 30 years ago; they're about Judge Kavanaugh today and how he is as a 53-year-old", Minority Leader Sen. 'I don't know. I don't know. "I know this because I heard Brett and his friends using these terms on multiple occasions". "I don't know", he said in front of laughing supporters. He said he disagreed with how Trump disparaged Ford, but, he added, "It can be worse. It would - in effect - be appealing the Senate's verdict directly to the American people".More news: Steelers Rumors: Teams Haven't Been Aggressive In Le'Veon Bell Trade Talks