But if leader Kim Jong Un does not agree to such a deal, Trump warned, the impoverished nation faces being decimated.
The president surmised that a change of tone this week by North Korea about the planned Trump-Kim June 12 summit in Singapore could be the result of a recent second meeting between Kim and Chinese President Xi Jinping.
"President Xi could be influencing Kim Jong Un," Trump, sitting alongside NATO Secretary-General Jens Stoltenberg in the Oval Office, told reporters.
If the summit is scrapped, "we go on to the next thing," added Trump.
Trump said planning discussions continue between U.S. and North Korean officials, who are behaving "like nothing happened," despite statements from Pyongyang casting doubt on the summit.
"They're dealing with us. We're working with them," Trump later reiterated during a Cabinet Room meeting with Stoltenberg and other U.S. and NATO officials.
North Korea's top negotiator, Ri Son Gwon, earlier Thursday denounced the South Korean government as "ignorant and incompetent," the latest in a series of inflammatory statements made by Pyongyang after it suddenly canceled talks with its southern neighbor amid U.S.-South Korean combat drills.
Asked by VOA News whether the Trump-Kim summit could proceed if talks between Pyongyang and Seoul did not resume, White House press secretary Sarah Sanders reiterated the Singapore talks were intended to be between only the United States and North Korea, but that the situation would be discussed with South Korean President Moon Jae-in when he visits the White House next week.
"Nothing has changed," Sanders later stated.
Others outside the White House, however, perceived that something had changed.
"The summit's dead. There's no question about it," asserted Harry Kazianis, director of defense studies at the Center for the National Interest, a public policy think tank in Washington.
The analyst said both sides probably hit an impasse about what the deliverables would be from the unprecedented meeting.
"I think what the North Koreans did — and it's pretty smart — they decided not to keep negotiating. They just decided to take it in a more public setting" and scrap the talks with Seoul, using the excuse of the ongoing South Korean-U.S. military exercises.
No talk of scaling back
U.S. Defense Department officials said there had been no discussion of scaling back the joint drills amid the concerns expressed by Pyongyang.
Asked by a reporter whether there was any consideration of reducing the scope of future drills to bolster prospects for negotiations with North Korea, Pentagon spokeswoman Dana White replied, "There has been no discussion of that."
Republican Senator James Risch of Idaho, a member of the Foreign Relations and Intelligence committees, remained optimistic that Trump would meet Kim.
"It should take place if both parties are acting in good faith, if both parties are able to reach a joint objective as to what they want to do," Risch told VOA's Korean service. "There's absolutely no reason that an agreement can't be reached, and it'll be better for everyone."
North Korea this week rejected any notion of a Libya-style deal in which it would give up all of its nuclear weapons in exchange for economic assistance from the United States and other countries.
Trump said Thursday that a Libya model was not under consideration by the United States.
The North Koreans, according to a number of analysts, expect to receive sanctions relief upfront before taking steps toward destroying any of its weapons of mass destruction, while American officials see a complete, verifiable and irreversible denuclearization as the starting point.
Kazianis pointed out that for the North Koreans, "nuclear weapons are all they have that would ever stave off regime change," which is the top fear of the leadership in Pyongyang.
People around Trump understand the classic process of summitry and the danger of throwing the two leaders together to just work it out, according to Kazianis.
"The risks would be astronomical, and if the summit blew up we could be right back on the brink to war again," he said. "And everybody has a vested interest in making sure that doesn't happen."
Risch, the Republican senator, said, "The world needs to try this to see if it works. The alternative is unthinkable. The bad ending that this was headed for can be avoided, and indeed, this is about the only street that takes us there."
South Korea said Wednesday's talks between it and the North were to have focused on demilitarization and plans to formally end the Korean War of the early 1950s.
Sustained hostilities on the Korean Peninsula ceased with an armistice, not a peace treaty, signed in 1953 by American, North Korean and Chinese officials. South Korea was not a signatory, and thus a technical state of war persists on the peninsula.