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.
He pledged that the full United States senate would begin voting on Mr Kavanaugh's nomination this week.
After filing a cloture petition, lawmakers must wait one legislative day before proceeding to the cloture vote, according to Senate rules.
If they don't have the votes, the nomination fails.
The members called for bipartisan ground rules to be established for public discussion of the information provided by the FBI, adding it is critical the American people have confidence in the FBI's investigation.
"The White House confirmation that it will not allow the FBI to interview Dr. Blasey Ford, Judge Kavanaugh or witnesses identified by Deborah Ramirez raises serious concerns that this is not a credible investigation", she said in a statement.
Senators Jeff Flake, Susan Collins and Lisa Murkowski - three moderate Republicans who could be pivotal in determining whether the Senate confirms Mr Kavanaugh - slammed Mr Trump's mocking imitation of Dr Ford's testimony as "appalling".
As supporters cheered him on, the president ridiculed Ford's emotional testimony before the Senate judiciary committee last week, where she conceded she could not remember certain details but vividly recounted the alleged assault by Kavanaugh.
Blumenthal told Wolf Blitzer on CNN's "The Situation Room" that "The clarification of that tweet would require me to go into the FBI report, but what that tweet highlights very dramatically and directly is the need for a full investigation, and for the public to know what's in that investigation, which is why it should be made public and why the facts here are really so important". 'I don't know.' Upstairs, downstairs, where was it?
"I had one beer, right?" I don't remember. Where is the place?
"A man's life is in tatters", he said.
"The president's comments were just plain wrong", added Collins.
The letter came in response to a tweet from Republicans on the committee which asserted that none of the previous six investigations into Kavanaugh's background unearthed evidence of alleged misconduct.
He also lamented the cost of Ford's allegations to Kavanaugh and insinuated that she was part of a conspiracy by the Democrats to discredit him.
The President's remarks also offered an opening to critics of the Kavanaugh nomination, including Democratic Sen. I don't remember. How did you get there?
A demonstrator holds a sign during a protest and march against the U.S. Supreme Court nominee Brett Kavanaugh in New York City.
"They're toast if they vote 'no, ' and they should be", Graham said.
But last week he took the gloves off, ripping into Democrats for what he called "a calculated and orchestrated political hit, fuelled with apparent pent-up anger about President Trump and the 2016 election" and "revenge on behalf of the Clintons." Sen. This background check, requested by a trio of senators who are undecided on Kavanaugh's confirmation, will be different.
'Wow, such enthusiasm and energy for Judge Brett Kavanaugh, ' Trump posted.
"To discuss something this sensitive at a political rally is just not right".