The Senate Judiciary Committee voted on Thursday to advance Kash Patel’s nomination to lead the F.B.I., paving the way for a floor vote on his confirmation as the bureau is racked by a bitter conflict between its temporary leaders and the Trump administration.

The vote, 12 to 10, fell along party lines. In forwarding Mr. Patel’s nomination to the full Senate, Republicans on the committee dismissed Democrats’ demands for an additional hearing to question Mr. Patel about a host of issues.

Those include grand jury testimony he gave in a criminal investigation of Donald J. Trump that remains sealed and whether Mr. Patel had been involved in a series of dismissals across the bureau. At his confirmation hearing, he denied knowing or remembering being part of any such discussions.

Mr. Patel, 44, has made attacking the F.B.I. a personal brand — in a book called “Government Gangsters,” in a series of television and podcast interviews, and in his longtime role as a trusted adviser to the president.

Republican lawmakers have embraced the choice of Mr. Patel, arguing that the F.B.I. treated conservatives unfairly during the Biden administration.

Senator Charles E. Grassley, Republican of Iowa and the committee’s chairman, said firings were needed at the F.B.I., which was “long overdue for massive reform.”