* Federal appeals court in D.C. has three vacancies
* Republicans say no need to fill vacant seats
* Obama dismisses Republican claims he is packing court (Adds detail and reaction)
Setting the stage for a political showdown with Senate Republicans, President Barack Obama named three lawyers on Tuesday to serve on a Washington federal appeals court often called the nation's second-most important court.
Senate Republicans have already objected to Obama filling the three vacant seats, saying there is no need because the court's case load, including major regulatory and other high-profile cases, is not sufficiently high.
Speaking in the White House Rose Garden with the three nominees by his side, Obama, a Democrat, urged the Senate to set aside politics and move quickly to hold confirmation votes.
"They have a constitutional duty to promptly consider judicial nominees for confirmation," he said. "Throughout my first term as president, the Senate too often failed to do that."
The president has picked Patricia Ann Millett, Cornelia Pillard and Robert Wilkins to fill three vacancies on the 11-seat U.S. Court of Appeals for the District of Columbia Circuit.
Millett is a Washington lawyer who regularly argues before the U.S. Supreme Court, Pillard is a professor at the Georgetown University Law Center and Wilkins is a judge on the U.S. District Court for the District of Columbia.
The latest nominees - two white women and an African-American man - reflect the White House's stated desire to increase diversity on a federal bench that remains largely occupied by white males.
A seat on the federal appeals court in Washington is sometimes seen as a springboard to serving on the Supreme Court. Appointments to both are for life.
A visibly agitated Obama at one point deviated from his prepared remarks when praising his nominees.
"These are no slouches, these are no hacks, these are incredibly accomplished lawyers by all accounts," he said. All three of the nominees attended Harvard Law School, as did Obama.
The president dismissed claims made by some Republicans that filling the three vacant seats constitutes "court-packing," a term used to describe President Franklin Roosevelt's effort decades ago to move the court to the left ideologically by increasing the number of seats on the Supreme Court.
"We are not adding seats here," Obama said. "We are trying to fill seats."
The president has had to fight to get his nominees to the court through the confirmation process. While Obama's fellow Democrats control the Senate, Republicans can hold up confirmation votes with procedural obstacles that require a supermajority of 60 of the 100 votes to be overcome.
One previous nominee, New York lawyer Caitlin Halligan, withdrew from consideration in March after Republicans blocked votes on her confirmation to the appeals court.
Last month, however, the Senate confirmed Sri Srinivasan, who attracted bipartisan support in part due to his service in the Justice Department under both Republican and Democratic presidents.
Once Srinivasan takes his place on the court, there will be eight active judges equally divided between Democratic and Republican appointees.
In his remarks, Obama stressed the importance of the court, noting that it has the final say on such issues as the environment and national security. "If we want to ensure a fair and functioning judiciary, our courts cannot be short-staffed," Obama said.
Some critics say Obama has been slow to fill the vacant seats. The White House only announced Halligan's nomination in September 2010, some 20 months after Obama took office, while Srinivasan was first nominated in the summer of 2012.
The first phase of the latest confirmation battle will take place in the Senate Judiciary Committee, which oversees judicial nominations and has long been a battleground for court nominees of presidents from both major parties.
Senator Patrick Leahy, the chairman, told Reuters at Tuesday's White House announcement that all three candidates are "enormously qualified" and that any opposition from Republicans would be "partisan in the extreme."
The senior Republican on the committee, Senator Charles Grassley of Iowa, has said he would object to further nominees to the appeals court. He introduced legislation that would strip the court of the three vacant seats, saying they are not needed.