"I want the FBI - this is now their seventh investigation - I want them to do a very comprehensive investigation", Trump said in the Rose Garden.
Kavanaugh has denied the allegations.
Kavanaugh has been accused of sexual assault by at least three women, including Dr. Christine Blasey Ford, who testified Thursday before the judiciary panel, reported The Hill.
The White House issued revised guidance to the FBI that agents can interview anyone they deem relevant as part of their investigation of Supreme Court nominee Brett Kavanaugh.
Sanders said Trump, who has vigorously defended Kavanaugh but also raised the slight possibility of withdrawing the nomination should damaging information be found, "will listen to the facts".
For the moment, the Supreme Court is one member short. But a vote on Kavanaugh's nomination has been delayed following allegations that he sexually assaulted a woman in high school.
Last Friday, Mr Trump ordered a one-week delay in a vote on Mr Kavanaugh so that the FBI could investigate the sexual misconduct claims.
"They should interview, but they should be guided by what the senators are looking for", he said.
Trump also says he thinks Kavanaugh spoke "very conclusively" and "very well" during his testimony last week, but says he was surprised by how vocal Kavanaugh was describing his alcohol use and how much he likes beer.
The White House on Friday directed the FBI to undertake a one-week investigation of the accusations at the request of the Senate Judiciary Committee.
Canada and the United States reach a deal on NAFTA
The US and Canada came to an agreement Sunday to tweak key pieces of the North American Free Trade Agreement, known as NAFTA . Reaching a deal would remove a key irritant in the trading relationship between the US and Canada, its top export market.
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Two minutes later, the Blues were ahead as Eden Hazard netted for the second straight game against Liverpool with a composed finish from close range.
R.I. senator says what he expects from Kavanaugh investigation
New York Senator Chuck Schumer, a Democrat, has been critical of Kavanaugh all week as well, calling for an FBI investigation. She's accused Kavanaugh and Judge of "abusive" behavior toward women and of being present at a party where she was raped.
Mr Trump on Saturday night also continued to fight back against the perception that world leaders diminished him last week by laughing at his claims of success at the United Nations General Assembly.
Kagan says nobody wanted to look "as if the court couldn't do its job". Trump asked, mentioning a term he has used in the past to denigrate Special Counsel Robert Mueller's investigation of Russia's role in the 2016 USA presidential election.
With the confirmation of Supreme Court nominee Judge Brett Kavanaugh in doubt, Justice Elena Kagan discussed how the court worked "super hard" in the past to overcome the unusual scenario of a 4-4 split it is due to encounter next week.
Speaking at a White House Rose Garden event Monday, Trump told reporters that he continues to support Kavanaugh. "It does no good to have an investigation that gives us more cover, for example".
Trump said he wants the Federal Bureau of Investigation probe "to be comprehensive".
Roche also said he believed Deborah Ramirez, another Yale classmate who claimed sexual misconduct against Kavanaugh.
Flake said he was in close touch with McGahn's office to ensure the investigation is thorough.
Coons and Flake said Kavanaugh's emotional but sharply partisan approach to his defense made them question his fitness for the highest court in the land.
Supreme Court nominations require Senate confirmation.