SEOUL (REUTERS/AFP) - US President Donald Trump and South Korea's new President Moon Jae-in spoke by telephone on Wednesday (May 10) and agreed to cooperate closely to resolve the North Korean nuclear crisis, the South Korean presidential Blue House said.

Trump told Moon that the North Korean nuclear issue was a complicated problem but one that could be resolved, the Blue House said in a statement.

The phone call marked the first contact between the two men.

Moon won South Korea's presidency in an election held on Tuesday, campaigning on a more conciliatory approach toward Pyongyang and ending nearly 10 years of hardline conservative rule in the South that focused on pressuring the reclusive North.

Trump invited Moon to visit the United States "as early as possible", according to the statement.

Moon backs engagement with the nuclear-armed North in the quest for peace - in contrast to the threatening rhetoric from the Trump administration in recent weeks - and has immediately declared his willingness to visit Pyongyang.

"If needed I will fly to Washington immediately," Moon said in an inauguration speech after taking the oath of office in front of lawmakers at Seoul's National Assembly building.

"I will also go to Beijing and Tokyo and even Pyongyang in the right circumstances."

But Trump recently appeared to offer the prospect of a diplomatic off-ramp last week, saying he would be "honoured" to meet North Korean leader Kim Jong-Un under the right conditions.