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WASHINGTON, DC - OCTOBER 04:  Comedian Amy Schumer waits to be led away after being arrested during a protest against the confirmation of Supreme Court nominee Judge Brett Kavanaugh October 4, 2018 at the Hart Senate Office Building on Capitol Hill in Washington, DC. Senators had an opportunity to review a new FBI background investigation into accusations of sexual assault against Kavanaugh and Republican leaders are moving to have a vote on his confirmation this weekend. (Photo by Alex Wong/Getty Images)
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WASHINGTON, DC - OCTOBER 04: Comedian Amy Schumer waits to be led away after being arrested during a protest against the confirmation of Supreme Court nominee Judge Brett Kavanaugh October 4, 2018 at the Hart Senate Office Building on Capitol Hill in Washington, DC. Senators had an opportunity to review a new FBI background investigation into accusations of sexual assault against Kavanaugh and Republican leaders are moving to have a vote on his confirmation this weekend. (Photo by Alex Wong/Getty Images)
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(CNN) —  

Senate Majority Leader Mitch McConnell took a key step to advance Brett Kavanaugh’s nomination to the Supreme Court on Wednesday, saying on the Senate floor that “this evening, the Senate will receive the results of the FBI supplemental background investigation” into the allegations against the nominee.

Late Wednesday evening, McConnell filed cloture, an action that moves the Senate closer to a confirmation vote, though a final vote would not take place until Saturday at the earliest.

Senate Republicans now need a simple majority for a vote to end debate on the nomination, which is expected to take place on Friday. If Republican lawmakers clear that hurdle, the Senate can then advance to a final confirmation vote on Kavanaugh’s nomination.

McConnell repeatedly vowed to hold a vote on the nomination this week and has said the results of the FBI investigation should not be a reason for delay, even as Senate Democrats have questioned the credibility of the investigation and called for more people to be interviewed as part of the probe.

The FBI inquiry began last week at the direction of the White House after Republican Sen. Jeff Flake of Arizona – a key vote on the nomination – called for it with the backing of Republican Sens. Lisa Murkowski of Alaska and Susan Collins of Maine.

Flake’s request followed wrenching testimony from Christine Blasey Ford, the first woman to go public with an allegation against Kavanaugh, who testified in front of the Senate Judiciary Committee that he sexually assaulted her at a social gathering during their high school years in the early 1980s. Kavanaugh also testified before the committee – and vehemently denied the allegation.

Other women have also come forward with allegations against Kavanaugh, including Deborah Ramirez, who told The New Yorker that she remembers Kavanaugh exposing himself to her at a dormitory party. Kavanaugh has denied all allegations against him.

CNN’s Phil Mattingly contributed to this report.