WASHINGTON — President Obama on Friday questioned Donald J. Trump’s fitness for office after statements from the Republican front-runner that the United States and its allies should move away from decades of constraints on the use of nuclear weapons. “We don’t want somebody in the Oval Office who doesn’t recognize how important that is,” Mr. Obama said.

Speaking to reporters at the end of a summit meeting devoted to nuclear security, the president said the comments by Mr. Trump reflected a person who “doesn’t know much about foreign policy or nuclear policy or the Korean Peninsula or the world generally.”

Mr. Obama has not hesitated to criticize Mr. Trump for contributing to a coarse tone and circuslike atmosphere on the campaign trail. But his criticism of the candidate’s comments on nuclear proliferation was not about public language or personal style, but about one of the gravest responsibilities of an American president. It carried an extra edge because it involved an issue that Mr. Obama has made a central goal of his presidency.

He said world leaders and other participants at the conference had expressed concerns about Mr. Trump’s comments during private conversations with him at the summit meeting, which gathered more than 50 world leaders to discuss ways to reduce the threat of a nuclear attack, whether from the leakage of nuclear fuel or the theft of a bomb by a terrorist group.