The withdrawal of the United States President Donald Trump from the planned summit with North Korean leader Kim Jong-un has caught many in South Korea off-guard, including President Moon Jae-in, with top diplomats scrambling to avert a political fallout with promises of continued talks.

According to the Korea Economic Daily, Moon said "The current communication method (between the US and North Korea) won't be able to resolve a sensitive and complex diplomatic issue. I look forward to seeing two leaders making a direct and close communication to resolve the current situation."

The announcement came just two days after Trump hosted Moon at the White House for talks widely seen as an effort to save the summit scheduled for next month in Singapore from being scuttled.

Relations between the two Koreas have warmed since Winter Olympics in February, when the North agreed to send its athletes to the South.

In April, Kim became the first North Korean leader to step into South Korea since the 1953 Korean War for an historic summit between Kim and Moon. The two leaders promised to work for denuclearisation of the region and pledged to sign peace deal.

South Korean Foreign Minister Kang Kyung-wha spoke on the phone with US Secretary of State Mike Pompeo, and received assurance that the US wants to keep the diplomatic channel with Pyongyang open, according to South Korea's Yonhap news agency.

Earlier, North Korean vice Foreign Minister Kim Kye-gwan said that despite Trump's decision to cancel the June 12 meeting in Singapore, Pyongyang has the "intent to sit with the US side to solve the problem regardless of ways at any time".

Still, politicians in Seoul did not hide their disappointment in the abrupt decision of Trump.

"It's a shame that there's a big obstacle in the process of the US-North Korea summit, but we believe the dialogue between the North and the US will be resumed," said Kim Hyun, spokesperson of the Democratic Party of Korea, the political party of Moon.