President Trump says Kim Jong Un "very much wants to" meet him at the Korean demilitarized zone in what would be an unprecedented display of goodwill between the U.S. and North Korea.

At the start of his second day in Seoul, Trump was asked if he had any updates after sending a surprise tweet that said he would like to shake Kim's hand at the border "and say Hello(?)!"

The president said it remains a possibility, hours after he indicated Pyongyang had responded to his offer.

“We’ll see. He very much wants to. We are tying to work it out," Trump said. "It will be very short, but that’s OK. A handshake means a lot."

Trump has a busy schedule for his Sunday, including meeting with South Korean President Moon Jae-in and visiting the U.S. Army Garrison Yongsan Landing Zone in Seoul.

His public schedule says his long-planned stop at the Korean Demilitarized Zone Overlook is set for 2:30 p.m., which will be 1:30 a.m. ET.

Trump has sought to build a relationship with the 35-year-old dictator, meeting first in June 2018 in Singapore and then in February in Vietnam. The second summit collapsed when Trump walked out over Kim demanding sanctions relief before dismantling his country's nuclear weapon program.

Since the second round of talks collapsed, North Korea has used at times harsh rhetoric. Last month, the state-run Korean Central News Agency called National Security Adviser John Bolton a "defective human product."

Trump added the brief stop in South Korea in mid-May, and journalists long suspected he would seek to meet Kim at the border.