North Korea on Sunday denied any recent correspondence with US President Donald Trump, less than a day after Trump mentioned having received a "nice note" from leader Kim Jong-un.

"The US media reported Saturday that the US President mentioned receiving a 'nice note' from our top leadership in a press conference," the North said in a statement carried by its outlet Korean Central News Agency.

"We cannot know for sure whether the US president reminisced about past correspondence, but our leadership did not send any letter to the US president recently."

Trump said during a daily White House press briefing on COVID-19 Saturday that he recently received a "nice note" from Kim, and insisted their relationship remains good.

The two countries have failed to make progress in denuclearization negotiations since a February 2019 summit between Trump and Kim ended without a deal.

But the leaders have maintained personal correspondence, with Trump sending a letter to Kim last month to offer US assistance with the coronavirus pandemic. (Yonhap)