Obama pledged earlier this month in the Czech Republic to cut the U.S. nuclear arsenal, bring the Comprehensive Test Ban Treaty into force and seek tough penalties for those that broke rules on nonproliferation.
On the first day of a two-day official visit to Finland, Medvedev said in a speech at Helsinki University that the topic of nuclear disarmament had become one of "high hopes."
"We noted what was said by the U.S. president in Prague that [disarmament] can be reached under a number of conditions," Medvedev said. "These conditions are fair, but I would want to cite more conditions needed to achieve such a treaty."
Both Moscow and Washington see a chance to "press the reset button" on thorny relations driven to post-Cold War lows during the administration of Obama's predecessor, George W. Bush.
Medvedev and Obama agreed at their first meeting in London this month to start joint work on a successor to the START-1 nuclear arms reduction treaty, which expires in December.
The first talks on the new pact will begin in Rome later this month.
Medvedev said Moscow's conditions include:
•A ban on deploying nuclear arms in space -- making it impossible to compensate for a cut in nuclear arms by building up of conventional forces.
?€?Making sure that nuclear weapons are destroyed and not just stockpiled.
He repeated Russia's longstanding concern about U.S. plans for a missile shield in Poland and the Czech Republic, a plan promoted under the Bush administration and condemned by Moscow as an act of aggression. Medvedev also repeated Russia's call for a new security pact to replace NATO, an idea that initially got a cool response when first broached at the OSCE's meeting in Helsinki in December.
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