The Russian president said that the Kremlin would like to help support efforts to resolve the North Korean nuclear standoff.
Putin told Kim that Russia supports his efforts to normalise North Korea's relations with the United States, adding that their talks should help better understand what Russia could do to support negotiations.
The pair smiled and shook hands before heading to talks at a university in Vladivostok.
Kim congratulated Putin on winning another six-year term in last year's election and noted that their talks will give a chance to exchange views on the situation on the Korean Peninsula.
The North Korean leader arrived by train dressed in a black coat and hat before meeting with local officials at Russia's Khasan train station near the border with North Korea.
Speaking to Russia's state-owned Rossiya-24, Kim said on arrival that he is hoping for a "successful and useful" visit and would like to discuss "settlement of the situation in the Korean peninsula" as well as bilateral ties with Russia.
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He then sat down with local officials as well as a Russian deputy foreign minister before setting off to the Pacific port city of Vladivostok for a summit with Mr Putin on Thursday.
He is the first North Korean leader to travel to Russia since his late father, Kim Jong Il, visited in 2011.
"I have heard a lot about your country and have long dreamt of visiting it," he was quoted as saying.
"It's been seven years since I took the helm, and I've only just managed to visit."
Kim evoked his father's "great love for Russia" and said he intends to strengthen ties between the two countries.
Earlier on Wednesday, the North's state media confirmed his departure aboard his khaki-green armoured train from an undisclosed location in North Korea.
Kim arrived later in Vladivostok for a dinner reception hosted by Russian deputy prime minister Yuri Trutnev, according to South Korean media.
After his summit with Mr Putin, Kim may tour neighbouring facilities or landmarks before departing for home on Friday, the reports said.
Kremlin adviser Yuri Ushakov told Russian media the summit will focus on North Korea's nuclear programme, noting that Moscow will seek to "consolidate the positive trends" stemming from Donald Trump's meetings with Kim.
In February, Kim's second summit with the US president in Hanoi ended without agreement because of disputes over US-led sanctions.
There have since been no publicly known high-level contacts between the US and North Korea, although both sides say they are still open to a third summit.
Kim wants the US to ease the sanctions to reciprocate some partial disarmament steps he took last year, but the US maintains the sanctions will stay in place until Pyongyang takes more significant denuclearisation steps.