North Korean leader Kim Jong Un has vowed to promote cooperative relations with Beijing in a letter to President Xi Jinping, the North's state media KCNA reported on Sunday.

The letter was in response to congratulations Xi sent for the North's founding anniversary this month where the president had expressed his willingness to strengthen strategic communication and working-level cooperation.

"I believe ... the DPRK-China friendly and cooperative relations would steadily develop in conformity with the requirements of the new era and the desire of the two peoples in the future," Kim said in the letter sent on Thursday.

DPRK is the initials of the North's official name, the Democratic People's Republic of Korea.

The North Korean leader left Russia last Sunday, wrapping up a six-day trip which has focused largely on military matters. (AFP)