Kim told Putin that Wednesday's meeting brought bilateral ties to a new level, and expressed his willingness to foster stable, future-oriented relations for the next 100 years, KCNA said.
The invitation from Kim for Putin came at the end of a reception hosted by the Kremlin chief after they toured the Vostochny Cosmodrome space centre and held talks on bilateral ties and boosting co-operation, KCNA said.
"At the end of the reception, Kim Jong-un courteously invited Putin to visit the DPRK at a convenient time," KCNA said, referring to the Democratic People's Republic of Korea, North Korea's formal name.
"Putin accepted the invitation with pleasure and reaffirmed his will to invariably carry forward the history and tradition of the Russia-DPRK friendship."
Both sides agreed to further strengthen strategic and tactical co-operation in the face of the "military threats, provocations and tyranny of imperialists," KCNA said.
Kim was briefed on technical details about Russian space vehicles during his visit to a cosmodrome, but there was no mention of any arms supplies, trade of weapons or technical assistance over weapons programs.
Following the reception, Kim "left for his next destination," KCNA said, without elaborating.
US and South Korean officials have expressed concern that Kim could 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 US State Department said the Biden administration "won't hesitate" to impose additional sanctions on Russia and North Korea if they conclude any new arms deals.
It was "troubling" that Russia is talking about co-operation with North Korea on programs that potentially would violate UN Security Council resolution, State Department spokesman Matthew Miller said, following the summit in Russia.
On Wednesday, Putin gave numerous hints that military co-operation was discussed but disclosed few details.Â
Defence Minister Sergei Shoigu attended the talks. The Kremlin said sensitive discussions between neighbours were a private matter.
When asked by Russian media on Wednesday if Russia would help Kim build satellites, Putin said: "That's why we came here."
For Russia, the summit was an opportunity to needle the US, the big power supporter of Ukraine, although it was unclear just how far Putin was prepared to go in fulfilling any North Korean wish lists of technology.
