The summit at the ar Eastern Federal University is the first high-level meeting between the two nations since 2011, when Kim's late father, Kim Jong-il, met the then Russian President Dmitry Medvedev, in eastern Siberia.
This is also the first time that Putin and Kim Jong-un is coming face-to-face.
Putin said he believed Kim Jong-un's visit would help "our bilateral relations and will help us to understand the ways we can help to settle the situation on the Korean peninsula, what can be done together, what Russia can do to support the positive processes that are taking their place now", reports CNN.
"We welcome your efforts on developing inter-Korean dialogue and your efforts on normalising the US-North Korean relations... In terms of bilateral agenda, we need to achieve a lot to develop trade and economic ties and humanitarian ties."
Speaking to the media after meeting Putin, Kim Jong-un said he expects to have a "beneficial meeting" with the Russian President.
He also thanked Putin for hosting him during a "very busy time" and added that the summit "will be very beneficial to constructively developing our two nation's relations which boasts a long history and tradition of friendship into one that is more firm and whole".
Kim Jong-un was greeted by Putin as the summit began with an official welcoming ceremony, after which the leaders are due to hold a bilateral meeting before being joined by their respective delegation, said Efe news.
The meetings are expected to focus on finding a peaceful resolution to the issue of Pyongyang's denuclearization and efforts at reducing cross-border tensions on the Korean peninsula.
The summit will also touch on bilateral issues between two nations who have previously enjoyed a much closer relationship.
The two nations were allies during the Cold War, a period during which the Soviet economic support effectively subsidizsd the existence of the North Korean regime.
Upon his arrival on Wednesday, Kim Jong-un said he hoped his meeting with Putin would be successful and that during the talks he hopes address issues related to the problems in Korean peninsula and the development of bilateral relations between Moscow and Pyongyang.
According to the Kremlin, the two leaders will focus their meeting on denuclearization efforts of the Korean peninsula at a time when talks between Washington and Pyongyang have been stalled following the failure of a summit in Hanoi in February between Kim and US President Donald Trump.
Putin is the sixth world leader to meet Kim Jong-un since he took control of North Korea in 2011.
Besides Putin and Trump, Kim Jong-un has also met Chinese President Xi Jinping, South Korean President Moon Jae-in, Singapore Prime Minister Lee Hsien Loong and Vietnamese President Nguyen Phu Trong.