The 53 Republicans voting include senators returning in the next Congress and newly elected Republicans who will not be sworn in until January. Retiring senators cannot vote but Vice President-elect J.D. Vance was able to; he will serve as president of the Senate in his new role and can vote to break any ties on the floor.

Two of the 53 Republicans did not vote on the first ballot, in which Mr. Thune had 23 votes, Mr. Cornyn had 15 and Mr. Scott had 13 votes.

Mr. Scott had the support of the grassroots MAGA movement and outside endorsements from top Trump surrogates, including Robert F. Kennedy Jr., Elon Musk and Vivek Ramaswamy. Mr. Trump did not weigh in.