The committee has endured accusations of political favoritism, hypocrisy and egregious error over several of the 98 prizes it has awarded to 131 laureates since 1901. Two committee members resigned in protest after Henry A. Kissinger was awarded the prize in 1973, a decision that provoked global outrage over the Nixon administration’s bombing campaigns in Vietnam, Laos and Cambodia. His co-winner and Vietnamese counterpart, Foreign Minister Le Duc Tho, refused to accept the prize, the only person to do so in the award’s history.

More than 20 years later, another committee member resigned when Yasir Arafat, the Palestinian leader, was included among the recipients for work on the Oslo Accords.

The prize has evolved in some cases as more of an acknowledgment of perseverance in the diplomatic battlefield, but criticism has remained over what is perceived in some cases to be a premature, even aspirational, award — the decision to name Mr. Obama a Nobel laureate for his “extraordinary efforts to strengthen international diplomacy and cooperation between peoples” less than nine months after his inauguration. (While Mr. Obama said at the time that he was not convinced that he deserved the award, the committee chairman at the time, Thorbjorn Jagland, later insisted that it remained one of the “proudest decisions” the committee had made.)

Some laureates argue that the international spotlight that followed their award offered an invaluable boost to their push for peace in their countries.

“In my case, the Nobel Peace Prize came like a gift from God,” President Juan Manuel Santos of Colombia said in an interview. Colombians had rejected his peace deal with a group of leftist rebels in 2016 just five days before he was announced as the winner for his efforts.

“When the Nobel Prize was awarded, everyone got very encouraged and supported what I was doing to renegotiate the peace agreement,” he said, which eventually passed through the country’s congress. “It was at a very opportune moment.” (Mr. Santos declined to comment on Mr. Trump’s nomination, citing continuing diplomatic relations with a presidential peer and respect for the committee’s deliberations.)

For José Ramos-Horta, the former president of East Timor, who received the prize in 1996, a nomination for peace talks on the Korean Peninsula would also expose the precarious judgment of potentially recognizing all parties involved in the diplomacy. Even more controversial than Mr. Trump and Mr. Moon would be Mr. Kim of North Korea: a reclusive dictator thought to have ordered the executions of disloyal officials including his own uncle, but an undeniable factor in any peace initiative between the countries.