Mr Trump and Mr Kim have traded insults over Pyongyang's nuclear and long-range missile programme, but the United States leader surprised the world last week when he said he was willing to talk to Mr Kim, the first time a sitting U.S. president and a North Korean leader have met. "We know they responded to that".
Later in the day, Trump himself tweeted out that there was, indeed, a deal "very much in the making". He says Russia, South Korea and Japan will as well. Summit meetings between national leaders usually take place only at the very end of negotiations, after lower-level bureaucrats have hammered out every detail of an agreement and scripted every pause and handshake in their public appearance.
But the biggest thing for me coming out of the news from the communist state, was that Kim wants a U.S. embassy in Pyongyang.
But less than 24 hours later, the White House appeared to hedge somewhat and call into question whether the meeting would ever come to fruition.
Brown and Portman both supported a bill previous year that imposed sanctions on North Korea for testing a long-range ballistic missile.
"I think certainly the administration has successfully put sufficient pressure on the North Koreans through China, though others, and through our own activity to hopefully bring the North Koreans to the table in a meaningful way", he said.
Kim has yet to publicly confirm his invitation to meet with Trump in a bid to defuse a standoff over Pyongyang's nuclear programme, and officials in Seoul and Washington say the exact location and timing of any summit remain to be determined.
Asked what Trump could accomplish by being nice to Kim, Republican Senator Ron Johnson of Wisconsin told CNN on Sunday, "Not a whole lot".
Among the unverified reports so far is that Kim hopes to sign a peace treaty with Trump - a long-held goal of the North Korean regime.
Sanders also denied that the Thursday announcement had been haphazard in any way or that key foreign policy officials had been left out.
"President Trump isn't doing this for theater".
There has been a stormy exchange of words between the two leaders, and at a campaign rally in Pennsylvania, President Trump indicated that North Korea is interested in pursuing peace.
"I just received an invitation last week to visit Korea as part of a congressional delegation, and I'm considering whether or not it can fit into the schedule to go", Faso, R-Kinderhook, said Monday.
Chinese President XI JINPING and I spoke at length about the meeting with KIM JONG UN of North Korea. China continues to be helpful!
Trump on Saturday predicted "tremendous success" in the talks and suggested North Korea wanted to "make peace".
Mr Suh is set to meet Japanese Prime Minister Shinzo Abe and Chief Cabinet Secretary Yoshihide Suga today, the spokesman added. Not fair or sustainable.
USA officials vowed Sunday they would not make any concessions to North Korea ahead of the summit and would continue to pressure North Korea.
The North Korean government has not tested nuclear weapons or long distance missiles since November of a year ago. It would likely be compared to former President Barack Obama's decision to kill or captured Osama Bin Laden, he said.