WASHINGTON — President Obama’s announcement of three nominees to an important federal appeals court on Tuesday is adding fuel to a larger fight on Capitol Hill over whether the minority party in the Senate has too much power to thwart a president’s agenda.

In a formal Rose Garden ceremony normally reserved for Supreme Court hopefuls and prominent cabinet nominees, Mr. Obama announced plans to fill, at the same time, all three vacancies on the Court of Appeals for the District of Columbia Circuit. Republicans quickly objected, saying that Mr. Obama and his Senate allies were trying to intimidate them into approving the nominees.

The fight has major implications for Mr. Obama’s agenda and legacy, the judicial system and Capitol Hill politics.

With these nominations, the White House is trying to install judges it hopes will be more ideologically sympathetic on a court that has overturned some important initiatives of the president’s first-term agenda on environmental, regulatory and labor issues.