The meeting on Sunday might "only be a handshake," said Trump. "But that's okay; a handshake means a lot."
"Some of you will join the fight on the Korean Peninsula ... where North Korea continues to threaten the peace," the vice president said.
Pyongyang's statement raises further doubts on whether leader Kim Jong Un will ever relinquish his arsenal.
South Korean President Moon Jae-in began his third summit with North Korean leader Kim Jong Un.
Operation Ulchi Freedom Guardian has reportedly been suspended after Trump's pledge to end "war games."
He also praised North Korea's state-run media and said it was kinder than Fox News.
Here's what North Koreans are being told about the Singapore summit.
The president said the important thing was "attitude," not whether he'd prepared for the meeting.
North Korea has conducted all six of its nuclear tests at the Punggye-ri site.
Kim Jong Un has pledged to close the country’s nuclear test site in May in full view of the outside world
North and South Korea committed to a "nuclear-free Korean Peninsula," but details were sparse.
"The two leaders declare before our people of 80 million and the entire world there will be no more war on the Korean peninsula and a new age of peace has begun," the declaration said.
For more than 60 years, an official peace treaty has remained elusive. Until now.
North Korea has told the United States it is prepared to discuss the denuclearization of the Korean Peninsula when Kim meets Trump, according to a U.S. official.
Experts believe Beijing is reeling from "exclusion anxiety" ahead of Pyongyang's denuclearization summits with Seoul and Washington.
Joseph Yun helped secure the release of American student Otto Warmbier last year.
Senior North Korean officials met with South Korean President Moon Jae-in at an undisclosed location in the Olympic city.