Conservative U.S. Supreme Court Justice Antonin Scalia has died, setting up a major political showdown between President Barack Obama and the Republican-controlled Senate over who will replace him just months before a presidential election.

Obama called Scalia, who served on the nation's highest court for nearly 30 years, a "larger-than-life presence" and said he intended to nominate someone to fill the vacant seat before leaving the White House next January.

"I plan to fulfill my constitutional responsibility to appoint a successor in due time and there will be plenty of time for me to do so and for the Senate to give that person a fair hearing and timely vote," Obama told reporters in California.

Scalia, 79, was found dead at the Cibolo Creek Ranch resort in West Texas on Saturday. He died of natural causes, according to Presidio County Judge Cinderela Guevara, who went to the ranch and saw the body.

Chief Justice John Roberts described his former colleague, who was known for his strident conservative views and theatrical flair in the courtroom, as an "extraordinary individual and jurist."

Obama ordered flags at the White House and all federal buildings to be flown at half-staff.

A number of leading Republicans, including Senate Majority Leader Mitch McConnell and Senate Judiciary Committee Chairman Chuck Grassley, immediately said they would oppose any attempt by Obama to nominate a new justice.

The political battle lines sharpened later at the Republican presidential debate in South Carolina, where front-runner Donald Trump and several of his rivals said it should be up to Obama's successor to replace Scalia.

"Delay, delay, delay," said Trump, who urged McConnell to block any Obama nomination.