Korean Workers' Party paper Rodong Sinmun reported Thursday the letter was delivered Wednesday to Assad to thank the Syrian leader for his congratulatory message to Pyongyang on April 15.
"I am confident the friendship and cooperation between our two countries will be further strengthened and developed, in accordance with the noble will of its leaders and the wishes of the people," Kim said in his letter to Assad.
The Rodong's disclosure of Kim's letter to the Syrian president comes a day after state media confirmed Kim had also sent a birthday message to Miguel Mario Díaz Canel Bermúdez, Cuba's president.
Seoul has dismissed speculation regarding Kim's health, following unconfirmed reports the North Korean leader was in critical condition following heart surgery last week.
On Wednesday, Vice Chairman of the Joint Chiefs of Staff Gen. John Hyten said he can neither confirm nor deny reports Kim is in poor health.
"In the intel, I don't have anything to confirm or deny anything along those lines, so I assume that Kim Jong Un is still in full control of the Korean nuclear force and the Korean military forces," Hyten had said. "I have no reason not to assume that."
Kim's letter to Assad was made public in North Korea the same day Rim Chon Il, North Korea's top diplomat on Russian affairs, published a statement on North Korea-Russia ties, South Korean news agency Yonhap reported.
Kim's first summit with Russian President Vladimir Putin in April 2019 laid a "solid foundation" for developing a "strategic and traditional friendship between North Korea and Russia," Rim said in his statement.
In the United States, NBA Hall-of-Famer Dennis Rodman voiced concerns amid rumors of Kim's health.
"I hope it's just a rumor that Marshal Kim Jong Un is sick," Rodman told TMZ Sports. "Hopefully I will find out more soon."
"I am praying for his speedy recovery, so that both my friends [President Trump and Marshal Kim] can continue toward a peaceful success."
Rodman last visited Pyongyang in 2017.