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Asked how long the FBI would have to investigate, Cornyn said not more than a week.

The Judiciary Committee said in a statement that it will ask the administration to instruct the FBI to conduct the investigation.

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

"As the Senate has requested, this update must be limited in scope and completed in less than one week," he added.

Senators are still expected to hold a procedural vote on Kavanaugh's nomination on Saturday. But a vote to end debate on Kavanaugh on Monday and hold a final vote on his nomination Tuesday are expected to be pushed back to allow the FBI investigation to wrap up.