At a news conference after the historic meeting with Kim in Singapore, Trump announced he would halt what he called "very provocative" and expensive regular military exercises that the United States holds with South Korea.
That was sure to rattle close allies South Korea and Japan. North Korea has long sought an end to the war games.
The two leaders promised in a joint statement after their meeting to work towards the "denuclearisation" of the Korean Peninsula and the United States promised its Cold War foe security guarantees, but they offered few specifics.
The summit, the first between a sitting U.S. president and a North Korean leader, was in stark contrast to a flurry of North Korean nuclear and missile tests and angry exchanges of insults between Trump and Kim last year that fuelled worries about war.
Noting past North Korean promises to denuclearise, many analysts cast doubt on how effective Trump had been at obtaining Washington's pre-summit goal of getting North Korea to undertake complete, verifiable and irreversible steps to scrap a nuclear arsenal that is advanced enough to threaten the United States.
Critics at home said the U.S. president had given away too much at a meeting that gave international standing to Kim. The North Korean leader is deeply isolated, his country accused by rights groups of widespread human rights abuses and under U.N. sanctions for its nuclear and ballistic missile programmes.
If implemented, the halting of the joint military exercises would be one of the most controversial moves to come from the summit. The drills help keep U.S. forces at a state of readiness in one of the world's most tense flashpoints.
"We will be stopping the war games which will save us a tremendous amount of money, unless and until we see the future negotiation is not going along like it should. But we'll be saving a tremendous amount of money, plus I think it's very provocative," Trump said.
His announcement was a surprise even to President Moon Jae-in's government in Seoul, which worked in recent months to help bring about the Trump-Kim summit.
The presidential Blue House said it needed "to find out the precise meaning or intentions" of Trump's statement, while adding that it was willing to "explore various measures to help the talks move forward more smoothly".
Pentagon officials were not immediately able to provide any details about Trump's remarks about suspending drills, something that the U.S. military has long resisted.
A spokeswoman for U.S. military forces in Korea said it had not received any direction to cease joint military drills.
"USFK has received no updated guidance on execution or cessation of training exercises - to include this fall's scheduled Ulchi Freedom Guardian," U.S. Forces in Korea spokeswoman Lieutenant Colonel Jennifer Lovett said in a statement.
One South Korean official said he initially thought Trump had misspoken.
"I was shocked when he called the exercises 'provocative,' a very unlikely word to be used by a U.S. president," the official said, speaking on condition of anonymity because it was a politically sensitive issue.
Current and former U.S. defence officials expressed concern at the possibility that the United States would unilaterally halt military exercises without an explicit concession from North Korea that lowers the threat from Pyongyang.
The U.S.-South Korean exercise calendar hits a high point every year with the Foal Eagle and Max Thunder drills, which both wrapped up last month.
'DIFFICULT TO DETERMINE'
The Republican chairman of the U.S. Senate Foreign Relations Committee, Bob Corker, said it was difficult to assess what had happened at the summit.
"While I am glad the president and Kim Jong Un were able to meet, it is difficult to determine what of concrete nature has occurred," Corker said in a statement.
Speaking about the military exercises, Corker told Reuters: "I don't know if that's an agreement or an ad hoc statement that was made. It wasn't in the agreement and sometimes things are said and walked back after talking to people at the Pentagon and other places."
U.S. House of Representatives Speaker Paul Ryan, a Republican, called North Korea a "brutal regime" and urged Trump to continue "maximum economic pressure" as negotiations advance.
U.S. Senate Democratic leader Chuck Schumer faulted Trump's agreement with Kim as short on details, saying the United States gave up "substantial leverage."
The two leaders smiled and shook hands at their meeting at the Capella hotel on Singapore's resort island of Sentosa, and Trump spoke in warm terms of Kim at his news conference afterward.
Just a few months ago, Kim was an international pariah accused of ordering the killing of his uncle, a half-brother and hundreds of officials suspected of disloyalty. Tens of thousands of North Koreans are imprisoned in labour camps.
The leaders' joint statement did not refer to human rights, although Trump said he had raised the issue with Kim, and he believed the North Korean leader wanted to "do the right thing".
Trump said he expected the denuclearisation process to start "very, very quickly" and it would be verified by "having a lot of people in North Korea".
He said Kim had announced that North Korea was destroying a major missile engine-testing site, but sanctions on North Korea would stay in place for now.
It was unclear if negotiations would lead to denuclearisation, or end with broken promises, as happened in the past, said Anthony Ruggiero, senior fellow at Washington's Foundation for Defense of Democracies think tank.
"This looks like a restatement of where we left negotiations more than 10 years ago and not a major step forward," he said.
The joint statement said Trump "committed to provide security guarantees" to North Korea and Kim "reaffirmed his firm and unwavering commitment to complete denuclearisation of the Korean Peninsula".
North Korea has long rejected unilateral nuclear disarmament, instead referring to the denuclearisation of the peninsula. That has always been interpreted as a call for the United States to remove its "nuclear umbrella" protecting South Korea and Japan.
Kim said after the summit he and Trump had "decided to leave the past behind. The world will see a major change."
Trump's meeting with Kim followed days of him berating traditional U.S. allies such as Canada and Germany in trade disputes. He left a Group of Seven summit in Canada early last weekend, and described host Prime Minister Justin Trudeau as "very dishonest and weak."
Trump and Kim's joint statement made no mention of the sanctions on North Korea and nor was there any reference to formally ending the 1950-53 Korean War, which killed millions of people and ended in a truce.
But it did say the two sides had agreed to recover the remains of prisoners of war and soldiers missing in action, so they could be repatriated.
Daniel Russel, formerly the State Department's top Asia diplomat under the Obama administration, said the absence of any reference to the North's ballistic missiles was "glaring."
"Trading our defence of South Korea for a promise is a lopsided deal that past presidents could have made but passed on," he said.
Trump said China, North Korea's main ally, would welcome the progress he and Kim had made.
Li Nan, senior researcher at Pangoal, a Beijing-based Chinese public policy think tank, said the meeting had only symbolic significance.
"There is no concrete detail on the denuclearisation of the Korean peninsula and the provision of security guarantees by the United States," Li said. "It is too early to call it a turning point in North Korea-U.S. relations."
Trump said he had formed a "very special bond" with Kim and relations with North Korea would be very different in future. He called Kim "very smart" and a "very worthy, very hard negotiator".
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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