Keen to revive its Soviet-era status as a world power, Russia is looking for new allies in the east at a time when its ties with the United States and the European Union remain sour.
Medvedev, who took over the presidency from his mentor Vladimir Putin this month, is due to head further east, to China, on Friday for the second part of his trip.
By contrast, Putin's first trip as Russian president in 2000 was to Britain.
Medvedev's talks on energy ties with Nazarbayev were due to include a Moscow-backed Caspian gas pipeline project, as well as space and military projects, but no concrete deals are expected to be signed.
Nazarbayev, who had warm personal relations with Putin, will be closely watching his 42-year-old Russian counterpart for clues to his leadership style.
Addressing him after a grand ceremony, Nazarbayev, in power for 18 years, called his relations with Russia "strategic".
"It's a great honour for us that you paid your first visit as president to Kazakhstan," he said.
A traditional Moscow ally, Kazakhstan is Central Asia's biggest economy and key to Russia's strategy of retaining its Soviet-era monopoly on regional energy exports.
Itself a booming oil economy with growing diplomatic ambitions, Kazakhstan has sought to balance its standing by forging closer ties with the West and China.
It has also hinted it may start buying military hardware from Nato allies.
Kazakhstan, where Russian remains an official language alongside Kazakh, has also irritated Moscow by suggesting it may take part in Western-proposed projects to ship its oil to Europe while bypassing Russia.
To counter these moves, Russia has struck a deal with Kazakhstan, Turkmenistan and Uzbekistan to revive a Soviet-era pipeline network that channels gas via Russian territory.