Shaking hands in front of the cameras, they then headed to talks at a university in Russia's far-eastern city of Vladivostok.
Putin, who did not elaborate on what kind of guarantees Kim wanted, said Russian Federation supported the United States call for complete denuclearization of the Korean peninsula.
The two men will sit down together on an island off the Russian Pacific city of Vladivostok two months after Kim's summit with US President Donald Trump ended in disagreement, cooling hopes of a breakthrough in the decades-old nuclear row.
The two leaders are also likely to discuss the fate of around 10,000 North Korean labourers working in Russian Federation who are due to leave by the end of 2019 under sanctions.
Kim's father, the late Kim Jong Il, met with Putin in Moscow in 2001 and in Vladivostok in 2002 when he led the reclusive regime. North Korea had blamed US Secretary of State Mike Pompeo after the two countries failed to reach a deal at the Hanoi summit.
Like the U.S., Moscow has strongly opposed Pyongyang's nuclear bid.
Mr. Kim arrived on Wednesday in Vladivostok on his armored train, saying upon arrival that he's hoping for a "successful and useful" visit.
Mr Putin said North Korea's leader was "fairly open" and had "talked freely on all issues that were on the agenda".
"[The exercises], far from trying to keep to preserve the valuable spark of peace, reconciliation and cooperation, have gone against the trend toward the reconciliation on the peninsular", a statement from North Korea's Government said.
Speaking to senior editors of the Asia News Network on the eve of the network's 20th anniversary, Moon said that he would do everything to ensure the success of any future meetings between the sitting U.S. president and the chairman of North Korea.
He also congratulated the Russian leader on his re-election to another six-year term last year.
Pyongyang has long viewed the exercises as a provocation and a rehearsal for an invasion of North Korea.
Moscow and Pyongyang have traditionally had close ties, although those relations became frayed somewhat after Russia's financial support was slashed following the collapse of the Soviet Union in 1991.
He congratulated his North Korean counterpart on being re-elected as the Chairman of the State Affairs Commission.