First, North Korea shocked Washington by lashing out at US-South Korea military drills, saying they could lead to the summit being scrapped.
"We'll have to see", Trump told reporters in the Oval Office when asked if the summit was still on.
The comments appeared to be a direct repudiation of statements by top Trump administration officials that North Korea must accept the total and irrevocable elimination of its nuclear arsenal before it could accept tangible benefits from the U.S. as part of any peace drive. "We will see what happens", he added.
State Department spokeswoman Heather Nauert said the US had not heard anything directly from North or South Korea that would change that.
Pyongyang had "made clear on several occasions that precondition for denuclearisation is to put an end to anti-DPRK hostile policy and nuclear threats and blackmail of the United States", minister Kim said.
"We believe this will help all parties to build mutual trust and create necessary conditions for solving problems through dialogue", he said. "The president's fully prepared and fully ready to carry on in these conversations both leading up to and if the meeting takes place", she said. "If not, that's okay".
The summit agreement, billed the Panmunjom Declaration, called for formally ending the 1950-53 Korean War within the year and pursuing "complete denuclearization" of the Korean Peninsula.
North Korea clashed with Bolton when he worked under the Bush administration, calling him "human scum" and a "bloodsucker".
North Korea's first vice minister of foreign affairs, Kim Kye Gwan, on Wednesday cast doubt on whether the planned meeting between leader Kim and Mr Trump, which is set for Singapore, would be held.
"High-ranking officials of the White House and the Department of State including Bolton, White House national security adviser, are letting loose the assertions of so-called Libya mode of nuclear abandonment", the statement read.
In a sign of the improved relationship, a North Korean delegation is visiting Beijing to learn about China's experience in economic reform and opening up. "The worst thing the White House could have done was to escalate the situation". It might have been infuriated over other USA demands for the scrapping of chemical and biological weapons in addition to its nuclear warheads and intercontinental ballistic missiles.
Trying to address the North Korean concerns, the president said that if Kim were to agree to denuclearize, "he'll get protections that would be very strong". He's gonna run this the way he sees fit. "But this time, they are not even getting to that point, they are already causing problems before we have the negotiation".