Viktor Yanukovich, the Ukranian president, has tilted Kiev's policies towards Moscow since taking over from Viktor Yushchenko, his pro-Western predecessor, in late February.
"Trade, business contacts, are becoming more active and this is due in no small part to the fact that the Ukrainian state now has another administration," Medvedev said.
The two leaders signed agreements on border demarcation, European security, co-operation between their respective intelligence services and the frozen conflict in the Moldovan breakaway region of Transdniestria, which has a border with Ukraine.
Last month, Yanukovich extended the lease of the Russian navy in Ukraine's port of Sevastopol until 2042 in return for cheaper gas.
His opposition to membership of Nato, which was ardently pursued by Yushchenko, has also endeared him to Moscow.
But Yanukovich's pro-Russian moves have reinvigorated the political opposition around Yulia Tymoshenko, the defeated presidential candidate and former prime minister.
Svoboda, the Ukrainian nationalist group, held a small demonstration in Kiev against Medvedev and Yanukovich in protest at what it said was the sell-out of the country's sovereignty.
Despite the goodwill between the two presidents, Yanukovich has also said he sees European integration as a priority for Ukraine.
He has been cool to a proposal from Moscow for a merger between Ukraine's energy holding Naftogas and Russia's state gas giant Gazprom.
Kiev wants to retain control of a network that is a conduit for 80 per cent of Russian gas supplies to the European Union and has noted that Vladimir Putin, the Russian prime minister, made his merger proposal with no advance warning to Ukraine.
On Monday, Alexei Miller, the head of Gazprom, stepped up pressure on Kiev, saying Russia would be ready to fund a complete overhaul of Ukraine's gas network if it agreed to the merger.
"The proposal to merge the two companies is fully in line with global trends to merge energy firms," Miller said.
"If Gazprom and Naftogaz merge, Gazprom can rely on its financial resources to fully modernise Ukraine's gas transportation system," he said.
Yanukovich, to Moscow's irritation, has suggested the European Union should be involved in any talk of a merger.
Asked about the issue last Thursday, Yanukovich said only Ukraine's fully equal participation in such a joint venture could be envisaged.
"Fifty-fifty, that would be the only way," he said.
Yanukovich favours pushing for the creation of a consortium involving the EU as well as Russia to modernise the ageing pipelines.