Washington (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.

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