Hosting Kim Yong Nam, North Korea's ceremonial head of state, Putin said the historic summit with the US president was "without doubt just the first step towards a full-blown settlement".
"Thanks to this meeting a possible negative scenario has been cast aside," Putin said.
"Certainly it creates conditions for further forward movement and decreases general tensions around the Korean peninsula," he added.
Trump and Kim made history on Tuesday holding a summit in Singapore. It was an unprecedented encounter that saw the leader of the world's most powerful democracy shake hands with the third-generation scion of a dynastic dictatorship.
But critics said the Kim and Trump summit was more style than substance, producing a document short on specifics about the key issue of Pyongyang's atomic weapons.
Putin said he would be happy to welcome Kim to Russia, suggesting they meet during an economic forum in the far eastern port city of Vladivostok this September.
The youthful North Korean leader has never visited Russia, unlike his father, Kim Jong-Il, who travelled to the country in his armoured train in 2011 for talks with Dmitry Medvedev, Russia's president at the time.
Russian Foreign Minister Sergei Lavrov became the first ever Russian official to meet Kim when he travelled to Pyongyang in late May.
The two countries share a short land border and have a history of long-standing ties.
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