"We hope. some of the high-level meetings that (the two sides) have been working towards can be held smoothly and. results can be achieved", he said.
A senior USA official told Associated Press news agency that there was a direction from the Oval Office to White House aides and other United States national security agencies to downplay the North Korean threats and not "take the bait" by overreacting to the provocation.
Earlier, the White House said it was "still hopeful" the summit would take place. "He'll be there and he'll be ready".
North Korean state media quoted vice foreign minister Kim Kye-gwan saying that If America "corners us and unilaterally demands we give up nuclear weapons we will no longer have an interest in talks and will have to reconsider whether we will accept the upcoming DPRK-US summit".
"If Kim goes to a summit and turns that down, he's responsible for the misery of the North Korean people", Thiessen said.
North Korea has also canceled high-level talks with South Korea that were scheduled for Wednesday local time over those same drills. In return United States would aid North Korean economy by lifting sanctions and allowing private capital to flow into the country. -South Korean "Max Thunder" air combat drills, which it said involved US stealth fighters and B-52 bombers.
The White House also sought to address a concern raised by the North Koreans with regards to the Libyan model of denuclearisation as has been indicated by national security adviser John Bolton.
The North has already canceled a planned meeting with South Korea.
The US state Department said that Washington will continue to prepare for the us-North Korean summit, despite threats from Pyongyang.
South Korea and the USA will be making a serious mistake if they believe they can get away with their "war rehearsals" in light of the North's recent efforts to improve relations with the South and hold talks with the US, it warned. 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.
The White House didn't immediately respond to a request for comment.
Press Secretary of the White house Sarah Sanders said that the U.S. alone the statement of North Korea, and will continue to closely coordinate its actions with its allies, according to Voice of America.
On Tuesday, a DPRK state media article published by the Korean Central News Agency (KCNA) announced the cancellation of a planned inter-Korean meeting on the same day over the Max Thunder joint U.S. -ROK military exercises now being staged in South Korea.