Asked on Wednesday whether the two leaders would talk about obtaining supplies from the North to replenish Moscow's dwindling stock of weapons and ammunition, Putin said they would discuss "all issues".
Washington and its allies believe defence co-operation is a top agenda item for the meeting.
"I am glad to see you," Putin said as he shook Kim's hand for about 40 seconds, welcoming him at Vostochny Cosmodrome, a modern space launch facility in the Amur region of Russia's Far East.
"This is our new cosmodrome."
Kim, speaking through an interpreter, thanked Putin for the invitation and for the warmth of his reception.
The summit between the leaders of the two countries, which have become increasingly isolated internationally, is being watched closely by Washington and allies, who suspect they could agree to trade arms and defence technology.
United States and South Korean officials have expressed concern Kim would provide weapons and ammunition to Russia, which has expended vast stocks in more than 18 months of war in Ukraine.
Moscow and Pyongyang have denied such intentions.
The choice to meet at Vostochny Cosmodrome - a symbol of Russia's ambitions as a space power - was notable, as North Korea twice failed to launch reconnaissance satellites in the past four months.
"That's why we came here," Putin said when asked by reporters whether Russia would help Kim build satellites.
"The leader of the DPRK shows great interest in rocket engineering.
"They are also trying to develop space."
Kim has made it a top priority to launch a spy satellite, as he pushes his nuclear-armed country to step up the development of ballistic missiles, drones and attack submarines.
In footage released by RIA news agency, Kim and Putin are seen shaking hands grinning broadly, standing outside, surrounded by security personnel and Russian media representatives, before walking together into a gleaming glass-walled building.
Television footage showed Putin giving Kim a tour of the facility.
Russian state television said Kim asked Putin a large number of detailed questions.
Russian media said Putin showed Kim around the building where Russia's new space launch rocket, the Angara, is assembled.
The 42.7-metre booster launches payloads into low earth orbit.
Hours ahead of the anticipated summit, North Korea launched two short-range ballistic missiles from an area near the capital, Pyongyang, into the sea off its east coast, South Korea's military and the Japanese government said.
It was the first such launch by the North while Kim was abroad, analysts said.
Kim has travelled outside the country only seven times in his 12 years in power, all in 2018 and 2019.
He also briefly stepped across the inter-Korean border twice.
Asked whether the leaders would discuss weapons, Kremlin spokesman Dmitry Peskov said the two countries co-operate in "sensitive" areas, which would not be made public, according to the Interfax news agency.
Humanitarian aid to North Korea and United Nations Security Council resolutions imposed on Pyongyang might also be discussed, Russian officials have said.
Kim arrived in Russia by private train on Tuesday with top defence industry and military aides and said his visit highlighted the "strategic importance" of the two countries' ties, the North's state news agency KCNA reported on Wednesday.
The make-up of Kim's delegation, with the notable presence of Munitions Industry Department Director Jo Chun Ryong, suggested an agenda heavy on defence industry co-operation, analysts said.
