The US hopes to see "major disarmament" of nuclear-armed North Korea by the end of President Donald Trump's first term in 2020, Secretary of State Mike Pompeo said Wednesday.

Speaking the day after an unprecedented summit between MR Trump and North Korean leader Kim Jong-un, Mr Pompeo told reporters in Seoul negotiations on Pyongyang's atomic arsenal could move forward quickly and would take place "most certainly in the president's first term".

"Major disarmament... We're hopeful that we can achieve that in the two and half years," he said, adding that there is "a lot of work left to do".

At the first-ever meeting between sitting leaders of the US and North Korea on Tuesday in Singapore, Mr Trump and Kim pledged in a joint statement to work toward the "complete denuclearisation of the Korean Peninsula".

However this stock phrase, favoured by Pyongyang, stopped short of longstanding US demands for North Korea to give up its atomic arsenal in a "verifiable" and "irreversible" way.

When questioned on the wording of the statement, Mr Pompeo said Wednesday that Mr Trump's intention was to allow the US the opportunity to pursue further productive conversations on the issue with Pyongyang.