WASHINGTON — Senate Republicans on Monday blocked President Obama’s third consecutive nominee to the country’s most powerful and prestigious appeals court and insisted they would not back down, inflaming a bitter debate over a president’s right to shape the judiciary.

By a vote of 53 to 38, the Senate failed to break a filibuster of Robert L. Wilkins, a federal judge who was nominated to fill one of three vacancies on the United States Court of Appeals for the District of Columbia Circuit, falling seven votes short of the 60 needed. Two Republicans — Lisa Murkowski of Alaska and Susan Collins of Maine — voted with the Democrats.

The impasse over Mr. Wilkins followed Republican blockades of two other candidates for the court since Oct. 31. Unlike previous fights over judicial nominees, the dispute is not as much about the judges’ individual political leanings as it is about the overall ideological makeup of the court. Republicans have raised few objections to the three candidates’ qualifications or legal positions.

Rather, Republicans are seeking to prevent Mr. Obama from filling any of the three existing vacancies on the 11-seat court, fearing that he will alter its conservative tilt. The court has immense political importance because it often rules on questions involving White House and federal agency policy.