Lee is the first South Korean leader to visit the Chinese capital in six years.

On Monday he met in Beijing with Xi, a day after the nuclear-armed North fired two ballistic missiles into the Sea of Japan.

Speaking to journalists in Shanghai as he wrapped up the visit, he said he had urged Beijing's help in bringing Pyongyang back to the negotiating table.

"I would like China to play a mediating role on issues related to the Korean Peninsula, including North Korea's nuclear program. All our channels are completely blocked," he said he told Xi.

"We hope China can serve as a mediator -- a mediator for peace," he added.

The Chinese leader in response urged Seoul to show "patience" with Pyongyang given how frayed ties between the two Koreas have become, Lee added.

"And they're right. For quite a long period, we carried out military actions that North Korea would have perceived as threatening," Lee said.

The South Korean leader also laid out a plan whereby Pyongyang would freeze its nuclear programme in exchange for "compensation".

"Just stopping at the current level -- no additional production of nuclear weapons, no transfer of nuclear materials abroad, and no further development of ICBMs -- would already be a gain," he said, referring to Intercontinental Ballistic Missiles.

"In the long term, we must not give up the goal of a nuclear?free Korean Peninsula," he added.

He said he had asked Beijing to convey this message to Pyongyang and that "there was consensus on these points from the Chinese".