President Moon Jae-in of South Korea has also called for an end-of-war declaration, which could put pressure on the United States to withdraw the nearly 28,500 troops stationed in South Korea — a move that the administration says it opposes. But it is uncertain how much progress toward denuclearization Mr. Trump is prepared to demand from Mr. Kim in exchange for a declaration of peace that would stop short of replacing the 1953 armistice.

Ned Price, a former spokesman for the National Security Council for President Barack Obama, on Monday warned of what he called a “Pollyannaish approach” by Mr. Trump that could lead the United States to give Mr. Kim too much in exchange for little real progress in abandoning his nuclear weapons.

“The chance for a diplomatic resolution to North Korea’s nuclear ambitions is too critical an opportunity to allow Trump to squander,” Mr. Price wrote in an email message Monday morning. “We must be comfortable holding the Trump administration’s feet to the fire.”

Senator Lindsey Graham, Republican of South Carolina, said it was Mr. Trump’s strong tactics that pushed Mr. Kim into negotiations in the first place. But in his own series of tweets on Monday morning, Mr. Graham described the upcoming talks in Hanoi as “our last, best chance to end the nuclear conflict with North Korea on peaceful terms.”