Kim made the request during his third meeting with Xi in Beijing last month, and the Chinese president promised to do his "utmost" to satisfy it, the Yomiuri Shimbun newspaper said.
"We are feeling great pain due to economic sanctions. Now that we have concluded the US-North Korea summit in success, I want (China) to work toward early lifting of the sanctions," Kim reportedly told Xi, according to the newspaper.
China says to play positive role as it seeks North Korea resolution
In recent months the Cold War-era allies have sought to repair ties strained by Pyongyang's nuclear tests and Beijing's support of subsequent UN sanctions.
Kim chose Beijing -- his main economic patron and diplomatic protector -- for his first official foreign trip in March and met Xi again in May in the northeastern port city of Dalian.
Kim asked Xi to help ease the sanctions that have crippled North Korea's economy, and urged China to back Pyongyang in its denuclearisation talks with Washington, the report said.
Xi in turn told Kim he "actively supports North Korea's reform and opening-up and will proactively cooperate with issues associated with the efforts", according to the Yomiuri.
North Korea says 'completely' dismantled nuclear test site
He also urged North Korea to "continue (its) consultations with China" as it negotiates with the United States, the report said.
China indicated last year that the UN Security Council could consider easing the punitive measures against Pyongyang.
Kim's third official visit to China was seen as a move to reassure Beijing that Pyongyang would not neglect its interests after the historic summit with Trump in Singapore.
China and the US both hope to see the Korean peninsula free of nuclear weapons.
North Korea tells US it is prepared to discuss denuclearisation
But Beijing is concerned Washington and Pyongyang might move closer at its expense, a possibility that China sees as threatening to its economic and security interests in the region
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ