"We will be stopping the war games which will save us a tremendous amount of money," Trump told reporters, adding he had agreed to stop the "war games" because he considers them "very provocative".
The US president also said he wants to withdraw American troops stationed in South Korea, like he had promised during his election campaign.
"I want to get our soldiers out. I want to bring our soldiers back home," Trump said, adding "But that's not part of the equation right now. I hope it will be eventually".
Trump's assertions could alarm South Korean conservatives who have urged him not to jeopardise their country's security.
The US and South Korea are security allies, with about 30,000 American troops based in country to defend it from its northern neighbour, which launched an invasion in 1950.
They hold joint military exercises every year that anger North Korea which has long demanded an end to the drills and frequently responds with volatile steps of its own, leading to a spike in tensions.
"I think it's very provocative. Under the circumstances we are negotiating a complete deal," Trump said, adding "It is inappropriate to have war games. Number one, we save money. A lot. Number two, it is really something they very much appreciated".
The move appears to be based on the 'freeze for freeze' proposal mooted by China, under which North Korea would stop nuclear and missile tests in exchange for a halt to the military exercises.
Kim has earlier declared a moratorium on testing, saying North Korea has completely developed its nuclear arsenal.
Trump and Kim today met for an unprecedented summit aimed at normalising bilateral ties and complete denuclearisation of the Korean peninsula.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)