The North Korean leader told his Russian counterpart they were fighting a sacred fight against western imperialism, while Mr Putin said the leaders would talk about "all the issues".
Mr Putin said he was "very glad" to see Mr Kim, with Kremlin footage showing the pair shaking hands enthusiastically at the Vostochny Cosmodrome spaceport in Russia’s far east.
The meeting came about an hour after North Korea fired two short-range ballistic missiles into the sea off its east coast.
South Korea’s Joint Chiefs of Staff did not immediately say how far the North Korean missiles flew. Japan’s Coast Guard, citing Tokyo’s Defence Ministry, said the missiles have probably already landed but still urged vessels to watch for falling objects.
The two men began their meeting at the Vostochny Cosmodrome, Russia’s most important domestic satellite launch centre, with a tour of a Soyuz-2 space rocket launch facility, at which Mr Kim peppered a Russian space official with questions about the rockets.
Mr Kim and Mr Putin then met together with their delegations and later one on one, according to Kremlin spokesman Dmitry Peskov.
Experts said Russia would probably use the talks to seek artillery shells and anti-tank missiles from North Korea, which wants advanced satellite and nuclear-powered submarine technology in return.
"We'll talk about all the issues, without haste. There is time," Mr Putin said, when asked whether military co-operation would be on the agenda.
"The leader of the DPRK [Democratic People's Republic of Korea] shows great interest in rocket technology, and they are trying to develop [their presence in] space," Mr Putin said, referring to North Korea by its official name.
In turn, Mr Kim praised Russia's "sacred fight to protect its sovereignty and security … against the hegemonic forces”.
"We will always support the decisions of President Putin and the Russian leadership ... and we will be together in the fight against imperialism," Mr Kim told Mr Putin.
He said North Korea’s relations with Russia were “the first priority”, adding that he was sure that the Russian army and people would triumph against "evil".
Later at an official dinner, Mr Putin toasted the "strengthening of future cooperation".
"A toast to the future strengthening of cooperation and friendship between our countries," Mr Putin said, raising his glass in footage aired by Russian state television.
"For the well-being and prosperity of our nations, for the health of the chairman and all of those present."
Ahn Chan-il, a defector-turned-researcher who runs the World Institute for North Korea Studies, said the relationship could have a significant effect on Russia's war in Ukraine.
"If North Korea's multiple rocket launchers and other artillery shells are provided to Russia in large quantities, it could have a significant impact on the war in Ukraine," he said.
The White House warned last week that Pyongyang would "pay a price" if it supplied Moscow with weaponry for the conflict.
Mr Kim, who travelled overland to Russia in his bullet-proof train, was accompanied by an entourage that suggested the summit would have a strong military focus.
Among the top military officials accompanying him were Korean People's Army Marshal Pak Jong-chon and Munitions Industry Department director Jo Chun-ryong, according to the North's state media.
What is the Vostochny Cosmodrome spaceport?
Located about 1,000km from Vladivostok, the site conducted its first launch in 2016, when a Soyuz-2 rocket blasted off.
The most recent launch was a Soyuz rocket carrying the ill-fated Luna-25 spacecraft, which crashed into the Moon.
Mr Putin ordered the construction of the cosmodrome to reduce reliance on the Baikonur Cosmodrome in Kazakhstan, which gained independence after the 1991 collapse of the Soviet Union.
The pair's meeting at Vostochny shines a spotlight on the West's concerns about the development of North Korea's missile capabilities, and sends a signal that Russia might help North Korea with its rocket and satellite programmes, experts said.
Pyongyang failed twice recently in its attempt to put a military spy satellite into orbit.
"The spaceport seems to be the optimal location because it responds to mutual interests, such as providing satellite technology requested by North Korea," Dr Ahn said.