"Such a visit is indeed on the agenda," said Dmitry Peskov. "We hope that the precise date and venue will be determined via diplomatic channels within the foreseeable future."
The announcement came as Kim makes his way back to Pyongyang following talks with US President Donald Trump in Vietnam, where the two sides failed to sign an agreement on denuclearisation or easing of sanctions on North Korea.
On Monday, Russian media reports said members of a parliamentary group that deals with Russia's relations with North Korea will visit Pyongyang on April 12.
Seoul proposes three-way talks
The proposal for the talks came during a National Security Council meeting on Monday, led by South Korean President Moon Jae-in, who said it was Seoul's "utmost priority" to prevent nuclear negotiations between the US and North Korea from derailing.
At the meeting, South Korea's Foreign Minister Kang Kyung-wha said the proposed talks, which could include civilian experts from the US and South Korea, would help settle differences over how much sanctions relief Washington should provide to North Korea in exchange for nuclear disarmament steps.
"We should look into what and how the US and North Korea see the current situation and we will come up with practical mediation measures," said Kang.
"We will come up with multiple measures to reopen dialogue between US and North Korea. In addition, we will cooperate with countries which are interested in the issue, such as China and Russia, to reopen the US-North dialogue as soon as possible."
Last week's meeting between Trump and Kim broke down over what the Americans said were North Korea's excessive demands for sanctions relief in exchange for a limited offer to shut down its ageing main nuclear complex in Yongbyon.
North Korea reportedly has other sites producing weapons-grade uranium hidden around the country.