Trump is making clear that he won't talk about US troop levels in South Korea during the planned meeting with Kim on June 12 in Singapore.
Speaking at the White House at a meeting with the president of Uzbekistan, he said the USA has not "heard anything" about threats to cancel the summit.
South Korea's Defense Ministry said Wednesday the two-week Maximum Thunder exercises, which began last Friday, would continue despite protests from North Korea.
South Korea is seeking to act as a mediator to bridge the gap between the United States and North Korea ahead of a planned summit, an official at South Korea's presidential Blue House said on Thursday. In that case, he added, Pyongyang would have to "reconsider" its participation at next month's summit in Singapore.More news: HTC U12+ revealed in new images while full specs leak out
"We haven't been notified at all", Mr Trump said.
If Pyongyang's statements caught Washington and Seoul off guard, they reflected a well-established North Korean position: that it is only willing to negotiate with the United States as a fellow nuclear power. He had given up his nuclear programme in the 2000s. Pyongyang's decision to cancel the inter-Korean summit also mirrors past North Korean criticism - which came even amid the 2018 diplomatic warming.
Ms Sanders said the North Korean demands were "not something that is out of the ordinary in these types of operations".
"The North's Korean Central News Agency said the Max Thunder drills between the South Korean and US air forces are a rehearsal for invasion of the North and a provocation amid warming inter-Korean ties", Yonhap reported.
Minister Kim also dismissed offers by US Secretary of State Mike Pompeo for US economic aid if the North denuclearizes.More news: Spielberg and DiCaprio in talks to reunite for Ulysses S. Grant biopic
It became a major setback in the reconciliation process on the Korean Peninsula, the basis for which was laid during a landmark meeting between the leaders of the two Koreas, the North's Kim Jong-un and the South's Moon Jae-in. Chairman Kim Jung Un has recently announced that he will allow foreign media to watch and record the dismantlement of the nuclear site in which all six nuclear weapons were detonated. The White House said plans for the summit were moving ahead.
"It's a diplomatic tactic", Kim Hyun-wook, professor at the Korea National Diplomatic Academy, told AFP, calling it "brinkmanship to change the United States position".
"Possibly the United States has put forward some unacceptable conditions, to which North Korea made a corresponding response using the military exercises as a pretext".
U.S. officials have repeatedly claimed credit for Washington's "maximum pressure" policy for bringing Pyongyang to the negotiating table. "The defensive nature of these combined exercises has been clear for many decades and has not changed", he said.
Ri said it will be hard to resume talks with South Korea "unless the serious situation which led to the suspension of the North-South high-level talks is settled".More news: Eagles' World Cup list good, says Okala
Pompeo, who returned from his second visit to Pyongyang last week with the freed Americans, has taken a softer line than Bolton, stressing the economic benefits, possibly including USA investment, that could flow to North Korea if it agrees to denuclearize.
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