The announcement came at the White House Friday after Trump met with a North Korean envoy.
White House press secretary Sarah Sanders said Trump met for 90 minutes with Kim Yong Chol to discuss denuclearization and a second summit. She said the president looks forward to meeting with North Korean leader Kim Jong Un at a place to be announced at a later date.
Trump had his first, historic meeting with Kim Jong Un last June in Singapore and reached a vague denuclearization agreement, but little tangible progress has been made since. So far, no details have been publicly released about how denuclearization could occur.
Vice Chairman Kim Yong Chol, a right-hand man to leader Kim Jong Un, opened talks with Trump little more than a year after the U.S. leader was threatening to wipe North Korea off the map.
Kim made the widely expected but previously unannounced trip to the White House -- which Trump spokeswoman Sarah Sanders said would discuss "continued progress on North Korea's final, fully verified denuclearization" -- after a meeting with Secretary of State Mike Pompeo that the State Department characterized as positive.
Kim Yong Chol is the first North Korean dignitary in nearly two decades to spend the night in Washington, staying at a fashionable hotel a short drive from the White House where Pompeo welcomed him near a framed portrait of civil rights icon Martin Luther King Jr.
Kim Jong Un and Trump held a landmark first meeting in Singapore in June where they signed a vaguely worded document, with Kim pledging to work towards the "denuclearization of the Korean peninsula."
But progress has since stalled as Pyongyang and Washington -- which stations 28,500 troops in South Korea -- disagree over what that means.
Trump has repeatedly voiced eagerness to see Kim Jong Un again -- even opining that the two are "in love" after their Singapore summit, the first meeting ever between sitting leaders from the two countries that never formally ended the 1950-53 Korean War.
Tensions began to abate a year ago with the encouragement of South Korea's dovish president, Moon Jae-in. Trump has repeatedly hailed his own diplomacy as a triumph, recently saying there would have been "a nice big fat war in Asia" if it were not for him.
Trump has said to expect an announcement soon about the second summit.
In Vietnam, a government source told AFP that "logistical preparations" were underway to host the summit, most likely in the capital Hanoi or coastal city of Danang, but that no decision had been made.
Prime Minister Nguyen Xuan Phuc said that Vietnam was ready to welcome the two leaders, noting that Hanoi has a growing relationship with the United States despite war memories.
"We don't know the final decision. However, if it happens here we will do our best to facilitate the meeting," he said in an interview with Bloomberg TV.
Kim, backed by ally China as well as South Korea, is also hoping for an easing of international sanctions, but the United States insists on maintaining maximum pressure until Pyongyang moves forward on giving up its nuclear weapons.
Although in Singapore Kim promised his "unwavering commitment to complete denuclearization of the Korean peninsula," the United States expects North Korea to give up nuclear weapons assembled over decades of work while Pyongyang more broadly seeks an end to what it sees as U.S. threats.
"I think there is somewhat of a general consensus of what denuclearization means. I think there is obviously still disagreement on how to get there -- whether denuclearization is the end of the process or the process itself," said Jenny Town, managing editor of the 38 North web journal on North Korea policy at the Stimson Center.
She noted that Americans have traditionally preferred to hash out the details of agreements before big summits, while the type of leader-driven diplomacy favored by Trump is more common in Asia.
"People have been very skeptical of this top-down approach, but we won't know unless we try it," Town said.