President Donald Trump has accepted an invitation to North Korea, according to Pyongyang's state-run media outlet.

Trump also extended a White House invitation to North Korean leader Kim Jong Un, which Kim accepted, the propaganda outlet said.

Trump first mentioned his intent to invite the Kim to the White House during their historic summit in Singapore a day earlier.

President Donald Trump has accepted an invitation to North Korea, according to Pyongyang's state-run media outlet.

North Korea's Korean Central News Agency (KCNA) claimed that Kim Jong Un invited Trump to visit Pyongyang at a "convenient time" and that Trump had invited Kim to the US.

"The two top leaders gladly accepted each other's invitation, convinced that it would serve as another important occasion for improved DPRK-US relation," KCNA said.

North Korea's claim follows the landmark summit in Singapore on Tuesday, where for the first time, a sitting US president met with a North Korean leader. Trump and Kim Jong Un shook hands in a made-for-camera moment, after launching a bevy of verbal threats in the previous year.

A Trump visit to Pyongyang, if it happens, would mark the first time a sitting US president enters the notoriously reclusive country.

Speaking to reporters at the summit, Trump said that he would "absolutely" invite Kim to the White House in Washington D.C.

"I know that we will have tremendous success together, and we will solve a big problem, a big dilemma that, until this point, has been unable to be solved," Trump said in his opening remarks to Kim. "I know that, working together, we will get it taken care of. So it's a great honor."

Kim replied: "We overcame all kinds of skepticism and speculations about this summit and I believe that this is good prelude for peace."

Following the meeting, the two leaders signed what was described as a "very comprehensive" document and broadly agreed to seek "comprehensive denuclearization of the Korean Peninsula." Details on how the two countries would achieve this goal were not mentioned during the document.

The White House did not respond to a request for comment on Tuesday evening.