WASHINGTON—President Barack Obama on Wednesday pointed to his Supreme Court nominee’s bipartisan support in the past, saying Merrick Garland deserves a swift hearing in the Senate, but defiant Republican leaders stuck to their opposition.

Mr. Obama’s nomination marks the latest and most significant turn in an election-year battle between the two parties over when to fill the critical ninth seat on the nation’s highest court, which has remained vacant since the death of Justice Antonin Scalia last month.

The nominee is expected to languish in the Republican-controlled Senate, where lawmakers on Wednesday quickly doubled down on promises not to hold hearings or votes until at least after the November elections.

The president, in announcing the nomination at the White House, warned the confirmation process for Judge Garland risks becoming another “extension of our divided politics.”

“Judge Garland has earned a track record of building consensus as a thoughtful, fair-minded judge who follows the law,” Mr. Obama said, as Judge Garland stood beside him in the Rose Garden.