Mr. Buttigieg outlined a process by which the North would take concrete and verifiable steps toward denuclearization by ceasing production of nuclear weapons materials and forgoing nuclear and missile tests, then dismantling production facilities and test sites, and finally destroying the weapons themselves.

In return, the United States would grant incremental relief from sanctions, encourage peace between North Korea and South Korea and normalize relations with North Korea, he said.

Making a case for engaging adversaries, Mr. Buttigieg said he would meet Mr. Kim to close a possible framework agreement setting the terms for negotiations but would not “bathe him in unwarranted compliments,” as Mr. Trump has done.

Senator Elizabeth Warren said she would put her immediate focus on an initial, verifiable agreement to prevent the expansion of North Korea’s arsenal and the transfer of its weapons to other countries. Real reductions in nuclear weapons and missiles and addressing human rights abuses would come later. She said she would meet Mr. Kim “if it is important to advance a substantive negotiation.”

Senator Cory Booker said that while he would empower American diplomats to negotiate with North Korea, “there is no indication that the current relationship between the U.S. and North Korea merits a meeting of the heads of state.”

And if such a summit were contemplated, North Korea would first have to meet conditions, such as dismantling the nuclear complex at Yongbyon, agreeing to formally end the Korean War and returning military remains, he said.

The responses from Joe Biden, Senator Kamala Harris and Beto O’Rourke added little new to the debate.