Medvedev appeared to suggest that Moscow was moving closer to backing fresh sanctions against Iran over its nuclear programme, saying that while such tactics were rarely productive they were sometimes "inevitable".
'Opportunity' for Iran
The apparent concord between Washington and Moscow on how best to address Iran's nuclear question comes days after the Obama administration announced that it would cancel plans to station missile interceptors and radar bases in Poland and the Czech Republic.
Russia had criticised that missile defence plan, saying that Washington was threatening its national security.
Obama said on Wednesday that Iran was running short of time in which to be open to the world on its sensitive nuclear work.
"Serious additional sanctions remain a possibility," he said, urging Tehran to "seize the opportunity" at the talks with the five permanent UN Security Council members and Germany.
Obama said the extra sanctions could come into force if Iran did not respond to serious negotiations.
The US president also said he and Medvedev shared the view that the Iran nuclear issue "should be resolved diplomatically."
Moscow and Washington are considering the scope of a new treaty to replace the Strategic Arms Reduction Treaty (Start), which expires in December.
"The work [towards a treaty] is under way … A good start allowed us to hope that our teams will cope and in due time we will have a document," Medvedev said.
In his speech to the UN General Assembly on Wednesday, Medvedev said that he and Obama viewed "verifiable and irreversible reductions" of nuclear weapons as an essential element in the improved relations between the two countries.