A divided Senate on Thursday voted to move toward confirming Pete Hegseth as secretary of defense, with the vast majority of Republicans voting in favor in a critical indicator that fresh allegations about his personal conduct are unlikely to derail his nomination.

On a 51 to 49 vote, Republicans broke a Democratic filibuster, clearing away the final hurdle to a confirmation vote now expected on Friday evening. The action came as Democrats, who have called President Trump’s nominee to lead the Pentagon unfit, worked to persuade a handful of G.O.P. senators to join them in opposition.

“We cannot risk installing a leader who may have a history that is exploitable by our adversaries,” Senator Jack Reed of Rhode Island, the top Democrat on the Armed Services Committee, said in a floor speech on Thursday. “Nor can we risk confirming a secretary of defense who has shown that he is incapable of being responsible, accountable and law abiding 24 hours a day, seven days a week, as that job requires.”

In his statement, Mr. Reed referred to a sworn statement submitted to the Senate on Tuesday by a former sister-in-law of Mr. Hegseth’s who described him as frequently intoxicated and “abusive” toward his second wife. Mr. Hegseth has denied the account, along with several other allegations that have dogged his nomination, including one of sexual assault, and other reports of excessive drinking.

A handful of Republicans have said privately that the new allegations from Danielle Diettrich Hegseth, the former wife of Mr. Hegseth’s brother, are concerning. But on Thursday, all but two voted to advance his nomination.

Senators Susan Collins, Republican of Maine, and Lisa Murkowski, Republican of Alaska, voted against moving forward with Mr. Hegseth’s bid. Before the vote, Ms. Murkowski said that she could not “in good conscience” support installing him at the Pentagon.