Senate Republican leaders announced Friday they have agreed to demands from two moderate Republicans to give the FBI a week to investigate sexual assault allegations against Supreme Court nominee Brett Kavanaugh.

Sen. John Cornyn, R-Texas, did not say when the Senate would hold a confirmation vote on Kavanaugh, but said he was optimistic a vote would happen. He also said the Senate would start the process by holding the first procedural vote on Kavanaugh Saturday at noon.

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The investigation into Kavanaugh would end after "no later than one week," Cornyn told reporters after a closed-door meeting with GOP lawmakers.

The Senate can't force the FBI to open an investigation. But the Senate Judiciary Committee announced Friday afternoon it would ask the Trump administration to "instruct the FBI to conduct a supplemental FBI background investigation" into Kavanaugh, and the White House is expected to allow it in order to get the nominee through the Senate.

The investigation, a statement said, "would be limited to current credible allegations against the nominee and must be completed no later than one week from today."

The announcement came after the Senate Judiciary Committee voted 11-10 to advance the nomination to the floor.

At the panel meeting, Sen. Jeff Flake, R-Ariz., indicated he would not be able to support Kavanaugh on the Senate floor without the investigation.

Senate Majority Leader Mitch McConnell, R-Ky., started the confirmation process for Kavanaugh on Friday evening, when the Senate moved to begin debate on Supreme Court nominee Brett Kavanaugh with a bipartisan voice vote.

A voice vote means senators do not have to remain in Washington to record their vote.

Flake said under the terms of the agreement, the second vote, a procedural hurdle known as cloture, won't be called until the FBI report is complete, which he expects will be by the one-week deadline.

Flake said the FBI would determine what allegation to examine - whether they should be limited to the accusation by Christine Blasey Ford or expanded to include two other claims dating back to Kavanaugh's teenage years.

"It shouldn't take that long," Flake said. "The leader won't have a cloture vote until the report is filed by the FBI."

Flake added, "It has to be done within a week or we move forward."

Flake noted that the FBI took just three days to examine the 1991 allegations by Anita Hill into then-Supreme Court nominee Clarence Thomas, who is now an Associate Justice.

"People out there need to know that we took every measure that we can within reason to ensure this process is worthy of this institution," Flake said. "I would love to see Judge Kavanaugh confirmed. I hope to do that. I want a better process."

Sen. Orrin Hatch, R-Utah, said he remains confident Kavanaugh can be confirmed.

"And he should be," he said.