WASHINGTON — US President Donald said on Wednesday that he has received a "great" letter from the top leader of the Democratic People's Republic of Korea (DPRK) Kim Jong-un and expected their second meeting to take place in the "not-too-distant future."

"I just got a great letter from Kim Jong-un," Trump told reporters at the White House during a Cabinet meeting.

"We'll probably now have another meeting ... we'll be setting that up in the not-too-distant future," added Trump, who revealed in early December that his second meeting with Kim was likely to happen in January or February.

Trump's words came one day after Pyongyang released a series of positive signals over the denuclearization of the Korean Peninsula.

Kim said on Tuesday in his New Year speech the he would push forward the denuclearization and was ready to meet with Trump at any time.

Kim also stressed his determination to work to build new relations with Washington on the condition that the United States takes corresponding measures.

"We could be left with no choice but to seek a new way if the US does not make good on its promises, misjudges our patience, while seeking to force things unilaterally and clinging to sanctions and pressure," Kim warned.

The relations between the DPRK and the United States improved last year. The first-ever summit between Trump and Kim was held in Singapore in June. Meanwhile, differences between the two sides remained over key issues like the scale of denuclearization, US sanctions, and whether to issue a war-ending declaration.