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The American flag flies at half-staff outside the U.S. Supreme Court building in Washington, D.C., U.S., Feb. 16, 2016, after Justice Antonin Scalia's unexpected death. Andrew Harrer/Bloomberg via Getty Images

The White House has narrowed its search for a Supreme Court nominee to three federal appeals court judges -- Sri Srinivasan, Merrick Garland and Paul Watford -- a source familiar with the selection process said on Friday.

Srinivasan and Garland are considered the leading contenders, according to the source and two other sources close to the process.

President Barack Obama is seeking a nominee to replace long-serving conservative Justice Antonin Scalia, who died on Feb. 13. Senate Republicans have vowed not to hold confirmation hearings or an up-or-down vote on any Supreme Court nominee put forward by Obama.

The process to select a replacement for Scalia appears to be nearing an end. It was unclear whether the other two other candidates who had been expected to be interviewed by Obama, federal appeals court judge Jane Kelly and federal trial judge Ketanji Brown Jackson, were now out of the running altogether.

Srinivasan, 49, and Garland, 63, are colleagues on the U.S. Court of Appeals for the District of Columbia Circuit. Srinivasan, who was born in India and grew up in Kansas, would be the first Asian-American and the first Hindu on the high court. Obama appointed him to the appeals court in 2013.

Garland is the chief judge of that appeals court, where he has served since being appointed by President Bill Clinton in 1997.

Watford, 48, is a judge on the San Francisco-based 9th U.S. Circuit Court of Appeals. He would be only the third black justice.