U.S. President Donald Trump said Saturday that he recently received a "nice note" from North Korean leader Kim Jong Un, while shrugging off concerns over the country's continued test-firing of short-range missiles.

"I see they're testing short-range missiles. And, you know, they've been doing it a long time," Trump said at a press conference at the White House, adding, "I received a nice note from him recently...I think we're doing fine."

Trump sent a personal letter to the North Korean leader, both countries said in late March. The latest communication received by Trump could be a reply from Kim, although the U.S. president did not explain its contents nor exactly when he received it.

The latest exchanges between the two leaders come at a time when negotiations to denuclearize North Korea remain stalled.

Trump also criticized claims that he has made concessions to North Korea, insisting at the press conference that he has "actually increased the sanctions" against the country.

But he said he has maintained amicable ties with Kim and that it is "not a bad thing to have a good relationship."

"Look, if I wasn't elected, you would, right now, be at war with North Korea," Trump claimed.

On Sunday, however, North Korea denied that Kim sent a letter to Trump, with an unnamed spokesperson of the country's Foreign Ministry saying, "There was no letter addressed recently to the U.S. president by the supreme leadership" of the nation.

U.S.-North Korea relations are "not an issue to be taken up just for diversion nor it should be misused for meeting selfish purposes," the spokesperson said in a statement carried by the state-run Korean Central News Agency.

The spokesperson added that Trump "could have referred to the personal letters that had been exchanged in the past, we are not sure."

Trump met the North Korean leader three times through June 2019. At the first-ever U.S.-North Korea summit in June 2018 in Singapore, Trump promised to provide security guarantees to Pyongyang in return for "complete" denuclearization of the Korean Peninsula.

But talks have since brought little progress, with the two countries at odds over issues such as how much sanctions relief should be extended to Pyongyang in return for denuclearization steps. In the meantime, North Korea has continued testing weapons.