US President Donald Trump will visit South Korea this weekend after an exchange of letters with North Korean leader Kim Jong-un boosted hopes for talks aimed at ending North Korea's nuclear program.

Trump is set to arrive in South Korea for a two-day visit on Saturday, and will meet President Moon Jae-in on Sunday, following a summit of G20 leaders in Japan, Moon's spokesperson, Ko Min-jung, said.

The announcement comes hours after US Secretary of State Mike Pompeo said he hoped a letter Trump sent to Kim could pave the way for a revival of stalled nuclear talks.

Trump and Moon would have "in-depth discussions on ways to work together to foster lasting peace through the complete denuclearization of the Korean Peninsula, while strengthening the two countries' alliance," Ko told a news briefing on Monday.

Pompeo, who spoke of Trump's letter to Kim before departing from Washington for the Middle East, said the US was ready to resume talks with North Korea immediately.

"I'm hopeful that this will provide a good foundation for us to begin ... these important discussions with the North Koreans," Pompeo told reporters.

Trump is considering a visit to the demilitarized zone (DMZ) separating the two Koreas, a South Korean official said. Trump wanted to go there during a 2017 trip to South Korea but heavy fog prevented it. Kim and Moon held their historic first summit in the DMZ last year, so a Trump visit to the border between the two Koreas this weekend could spark speculation of a meeting with Kim there.

Another official in the South Korean presidential office said she was not aware of any plan for Trump to meet Kim.

Trump and Kim held their first summit in Singapore in June last year, agreeing to establish new relations and work toward the denuclearization of the Korean Peninsula. But a second summit in Vietnam in February ended without reaching an agreement.