Kim Jong-un has received an “excellent” letter from Donald Trump, North Korean state media reported, and will "seriously contemplate the interesting content".
Mr Kim, 35, was pictured reading the letter, the contents of which were not disclosed.
But the North Korean leader was evidently impressed by the letter and its author, praising Mr Trump’s "extraordinary courage".
Earlier this month, Mr Trump said a “beautiful” letter had been sent to him by Mr Kim.
The letter exchange is the latest chapter in efforts to find common ground between the two countries.
Talks between the US and North Korea stalled in February, after a meeting in Vietnam – the second encounter for the two men – ended with no agreement reached.
The US is demanding that North Korea abandon its nuclear weapons entirely before international sanctions are lifted. North Korea is seeking a step-by-step approach in which moves toward denuclearization are matched by concessions from the US, notably a relaxation of the sanctions.
Mr Trump and Mr Kim met face-to-face for the first time in June 2018, in Singapore.
South Korea’s presidential office said it sees the exchange of letters between Mr Kim and Mr Trump as a positive development for keeping the momentum for dialogue alive.
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News of Mr Trump’s letter came days after Mr Kim’s summit with visiting Chinese President Xi Jinping, which experts say underscored China’s importance in the diplomatic push to resolve the nuclear standoff with the North.
North Korean state media said Mr Kim and Mr Xi discussed the political situation surrounding the Korean Peninsula and reached unspecified consensus on important issues.
Mr Xi is expected to meet with Mr Trump next week in Japan during the G-20 summit. Analysts say he could pass him a message from Mr Kim about the nuclear negotiations.
Mr Kim said during his New Year’s speech said he would seek a “new way” if the United States persists with sanctions and pressure against North Korea.
After the collapse of his meeting with Mr Trump in Hanoi, Mr Kim said Washington has until the end of the year to offer mutually acceptable terms for a deal to salvage the negotiations.