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President Barack Obama on Tuesday repeated his vow to nominate a "well qualified candidate" to the U.S. Supreme Court following the death of Justice Antonin Scalia.

Many Republicans, including Senate Majority Leader Mitch McConnell, have said the next president should nominate Scalia’s successor, and some have vowed to block hearings for any Obama nominee.

But "the Constitution is pretty clear about what is supposed to happen now," Obama said Tuesday at a press conference following the U.S.-Association of Southeast Asian Nations summit in Rancho Mirage, California. "When there is a vacancy on the Supreme Court, the president of the United States is to nominate someone, the Senate is to consider that nomination, and either they disapprove of the nominee or that nominee is elevated to the Supreme Court."

"Historically, this has not been viewed as a question," Obama said.

"There’s no unwritten law that says that it can only be done on off years, that’s not in the constitutional text," Obama said. "I’m amused when I hear people who claim to be strict interpreters of the Constitution suddenly reading into it provisions that are not there."

After Scalia's death on Saturday Obama said "I plan to fulfill my constitutional responsibilities."

An Obama appointment to the Supreme Court could swing the court to a liberal majority. Because justices serve life terms, the next judge could have a decades-long impact on the court.

Related: Obama Could Win Supreme Court Battle in This 17-Day Window

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A leading Supreme Court analyst said U.S. Attorney General Loretta Lynch is the "most likely candidate" to be chosen by Obama.

D.C. Circuit Judge Sri Srinivasan, California Attorney General Kamala Harris and Patricia Millett, a judge on the U.S. Court of Appeals for the D.C. Circuit, have also been mentioned by analysts as possible picks.

"We’re going to find somebody who is an outstanding legal mind, somebody who cares deeply about our democracy and cares about the rule of law,” Obama said.

"There is not going to be any particular position on a particular issue that determines whether I nominate them,” Obama said, adding that he will nominate someone “indisputably qualified for the seat.”

Related: Scalia's Death Has 'Refocused' Race, Rubio Says

Asked whether he would consider a recess appointment, Obama said, "I think that we have more than enough time to go through regular order, regular processes."

"I intend to nominate someone, to present them to the American people, to present them to the Senate, I expect them to hold hearings, I expect there to be a vote. Full stop,” Obama said.

Scalia was found dead in his room at a private ranch in Texas Saturday, and his death was determined to be from natural causes and no autopsy was conducted, a judge told The Associated Press. He was 79.

Scalia’s body will lie in repose Friday in the Great Hall of the Supreme Court building.

Related: Obama's Election Year Supreme Court Nomination Is Not Unprecedented

Five of the six Republican presidential candidates said at Saturday’s debate that the president should not nominate a judge to the Supreme Court or called on the Senate to block any nominee. Jeb Bush said Obama "has every right" to nominate someone, but said Obama should choose a consensus candidate.

Obama said Tuesday that he will nominate a well-qualified candidate and expects the Senate to hold hearings and vote on the nominee.

Obama and other members of his administration voted to filibuster the nomination of Justice Samuel Alito in 2006 when they were in the Senate. Alito was confirmed.

Asked whether that undercuts his position, Obama said, “How judicial nominations have evolved over time is not historically the fault of any single party. This has become just one more extension of politics."

But he added: "Historically, if you look at it, regardless of what votes particular senators have taken, there's been a basic consensus, a basic understanding that Supreme Court's different. And each caucus may decide who's going vote where and what, but that basically you let the vote come up and you make sure that a well-qualified candidate is able to join the bench — even if you don't particularly agree with them. And my expectation is that the same should happen here."

"This will be a test, one more test, of whether or not norms, rules, basic fair play can function at all in Washington these days," Obama said.