Donald Trump has sent a letter to North Korea’s leader, Kim Jong-Un, expressing his willingness to help the North battle the coronavirus, North Korea claimed on Sunday.

“I would like to extend sincere gratitude to the US president for sending his invariable faith to the chairman,” said Kim Yo Jong, the North Korean leader’s sister and policy aide, in a statement carried by the country’s state-run Korean​ Central​ News Agency. She lauded Mr Trump’s decision to write the letter as “a good judgment and proper action”.

In the letter, Mr Trump “wished the family of the chairman and our people well-being”, she said, referring to her brother by one of his official titles.

The White House confirmed that Mr Trump had sent Kim Jong-un a letter but did not comment on its specifics.

Mr Trump and Mr Kim have repeatedly touted their unusual relationship. They exchanged a number of personal letters before and after their first summit in Singapore in 2018, and at one point Mr Trump said he and Mr Kim had fallen “in love”.

But relations between Pyongyang and Washington ​have cooled since the leaders’ second summit, held in Vietnam last February. Talks collapsed over differences regarding how quickly North Korea should dismantle its nuclear weapons program and when Washington should ease sanctions.

Since then, Mr Kim has repeatedly said that North Korea was no longer interested in diplomacy with the United States unless it changed what he called its hostile policy, including sanctions. He also warned that the country no longer felt bound by its self-imposed moratorium on testing nuclear weapons and long-range ballistic missiles​.

On Saturday, Mr Kim attended the testing of two short-range ballistic missiles by ​his military.

Kim Yo Jong said Sunday that her brother had “mentioned his special personal relations with Mr Trump again and appreciated the personal letter.” But she said good personal relations between the two leaders were not enough to improve their countries’ ties.

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A senior Trump administration official, who insisted on anonymity, said the president’s letter was consistent with his efforts to engage with world leaders during the coronavirus pandemic.

Officially, North Korea has reported no coronavirus cases, ​although it says it is waging an all-out campaign against the virus.​ Outside health experts fear that the country might be hiding an outbreak.