The Mediterranean island, waiting for a multi-billion euro bailout after heavy exposure to debt-crippled Greece, has had to contend with misgivings from lender states on how committed it is to fighting money laundering and why the island is a magnet for Russian money.
Cyprus offers the eurozone's lowest nominal corporate tax rate and has had close political ties with Russia for decades.
"We think the main burden to solve these problems should be taken on by Cyprus and the EU states," Medvedev said in an interview with the German business daily Handelsblatt on Monday (28 January).
"But we are not refusing to help under certain conditions. The conditions must be agreed first. Before that, there can be no money from us," he added, adding that Russia had already given Cyprus a €2.5 billion loan in 2011.
Cyprus sought a bailout from the EU and the IMF last year, but aid has stalled as they assess the precise capital requirements of its banking system and whether the government may have to sell state assets to ensure the bailout is not too onerous to be paid back.
The incumbent government is against asset disposals but presidential elections will be held in mid-February.
In November, Der Spiegel magazine cited a German intelligence agency report as saying "Russian oligarchs, business people and mafiosi" would benefit most from any bailout and that Cyprus was a "gateway for money laundering in the EU".
Cyprus says it has strengthened its regulations against money laundering over the past decade and is in full conformity with international rules.
Medvedev also said that Russia had no intention of buying sovereign debt from eurozone countries, but that he was positive on the euro.
"Even though the euro is currently in a dismal state, I am of the view that the euro helped the whole global economy and global finances in the crisis of 2008/09," he said.
"The idea of the euro is generally positive. That's why I hope it will have a positive future," he said.