His North Korean counterpart said he hoped for further "development of our relations" in comments translated into Russian.
After the meeting, Lavrov answered questions from journalists alone, saying the ministers "examined in some detail" the nuclear situation on the peninsula.
"The Russian side confirmed that we welcome gradual normalisation of the situation, an end to mutual threats and readiness for contact between the two Koreas as well as between North Korea and the US," Lavrov said.
He said that upcoming talks should aim at denuclearisation of the Korean peninsula, but stipulated that Pyongyang must also receive "cast-iron guarantees" of its security.
He added that he had accepted an invitation for a return visit to Pyongyang, without giving a date.
Alexander Vorontsov, a specialist on the Koreas from Moscow's Oriental Studies Institute, said it was "particularly important (for Pyongyang) to enlist support, including from Russia, to cover its back" before further summits.
The leader's secretive three-day meeting with Chinese President Xi Jinping in March was his first trip abroad since gaining power from his late father in 2011. China is North Korea's main trading partner.
The visit was seen as a gesture of reconciliation after months of high tensions over the North's missile and nuclear programmes.
Kim is due to hold a summit with South Korea's Moon Jae-in on April 27 in the Demilitarized Zone that divides the Korean peninsula, in only the third meeting of its kind.
The stunning detente with the US comes after North Korea last year fired multiple missiles and carried out its most powerful nuclear test.
Trump in turn hurled insults at Kim, calling him a "madman with nuclear weapons" and said that a military option against North Korea was "locked and loaded".
If the summits with Moon and Trump are a success, "it will be a turning point, a breakthrough," said analyst Vorontsov.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)