RANCHO MIRAGE, Calif. — President Obama on Tuesday challenged Republicans to offer a plausible rationale for refusing to consider a Supreme Court candidate to replace Justice Antonin Scalia, and he pledged to nominate someone with an “outstanding legal mind” who cares about democracy and the rule of law.

“The Constitution is pretty clear about what is supposed to happen now,” Mr. Obama said during a news conference after a meeting in California with leaders of Southeast Asia. He said the Constitution demanded that a president nominate someone for the court and the Senate either confirms or rejects. “There’s no unwritten law that says that it can only be done on off years,” Mr. Obama said. “That’s not in the constitutional text.”

But Mr. Obama — who defended his own role in an effort to block a confirmation vote on Samuel A. Alito Jr. in 2005 — said he understood the political stakes of a nomination that could change the balance on the court. “I understand the pressure that Republican senators are now under,” he said. “This would be a deciding vote.”

Image President Obama said, “The Constitution is pretty clear.” Credit... Kevin Lamarque/Reuters

Mr. Obama’s remarks were his first extensive public reaction to the political forces unleashed by the death last weekend of Justice Scalia, and they offered a glimpse of how he intends to use the power of the presidency to raise pressure on Republicans to hold hearings on whomever he nominates for the court.