Sen. Lindsey O. Graham (R-S.C.) urged Democrats on Sunday to get on board with authorizing military force against North Korea if diplomatic efforts fail. (Andrew Harnik/AP)

Two top senators indicated Sunday that they generally agree on what a good nuclear deal with North Korea might look like, but they differed sharply on whether to back it up with a military Plan B.

Sen. Lindsey O. Graham (R-S.C.), a leading Republican hawk, said in an interview on ABC’s “This Week” that he’s “100 percent” pleased with a letter top Senate Democrats sent President Trump last week insisting that any deal with North Korea must include a permanent dismantling of the country’s nuclear and ballistic-missile programs.

But Graham also called on his colleagues to go a step further and authorize use of military force if diplomatic routes fail.

“Here’s what I would say to my Democratic colleagues,” Graham told host George Stephanopolous. “I appreciate you telling the president what a good nuclear deal would look like, but the country needs you to back the president up to get that deal.”

“So here’s my question for my Democratic colleagues,” Graham continued. “If diplomacy fails, will you support my efforts to authorize the use of military force as a last resort to convince North Korea and China things will be different this time?”

Lawmakers and policymakers are closely watching this week’s historic summit in Singapore between Trump and North Korean leader Kim Jong Un. The two men are expected to discuss North Korea’s nuclear and missile capabilities, which the country has rapidly advanced during the past year under Kim’s watch. Kim appears especially interested in getting rid of international sanctions that are hampering his country’s economic growth.

Sen. Robert Menendez (N.J.), the ranking Democrat on the Senate Foreign Relations Committee, said he’s not ready to back a congressional Authorization for Use of Military Force until he is confident “the path to peace really isn’t obtainable” without military action.

“I love my friend Lindsey Graham, but I think first we have to give a chance at peace, and that’s why we outlined very clearly what a successful agreement would be,” Menendez said. “A complete, irreversible denuclearization” for the Korean Peninsula.

Menendez was a signatory to the letter to the president last week, which lists several conditions Democrats say must be part of any deal the two countries might strike. They urged Trump to maintain a tough stance with Kim and his ally China, writing that any deal giving North Korea relief on sanctions without the ability to verify that it is dismantling its nuclear and missile arsenal “is a bad deal.”

Asked by Stephanopolous whether Trump deserves credit for brokering the first meeting in recent history between a sitting U.S. president and a North Korean leader, Menendez said he is worried Trump “thinks this is a mano-a-mano engagement in which he can achieve the success we want.”

“We want him to succeed, but I think success has to be defined not as a grand moment in which you say we have peace in our time when we don’t have the verifiable elements of a denuclearization,” Menendez said.