Obama told reporters after meeting Medvedev in the Danish capital that Washington and Moscow were quite close to agreement but a senior Kremlin official later said that talks would continue in January after a Christmas break.
There will be a little break -- they (the Americans) will have Christmas holidays, then we will have ours, the Kremlin's top foreign policy adviser Sergei Prikhodko told reporters.
Neither side disclosed details of why the talks on a successor to the 1991 START I pact had missed a December 5 deadline and have still not produced a result, even after the two leaders met on the fringes of the U.N. climate conference in Copenhagen.
The world's two largest nuclear powers have been trying since April to find a replacement for START I, which led to the biggest cuts in atomic weapons in history.
The initiative forms the centerpiece of Obama's efforts to reset relations with Russia after a tense period during the administration of his predecessor George W. Bush.
The U.S. leader has abandoned plans to station anti-missile systems in Central Europe and toned down Washington's support for former Soviet republics Ukraine and Georgia to join NATO, moves designed to please Russia.
In return Obama wants Moscow's help on a wide range of international issues ranging from Iran to North Korea to Afghanistan.
Obama was careful to avoid any mention of disagreements in his remarks after speaking to Medvedev.
We've been making excellent progress. We are quite close to an agreement. And I'm confident it will be completed in a timely fashion, he said.
Medvedev said that there were certain technical details ... which require further work but did not elaborate.
One of the key issues dividing Moscow and Washington has been how to verify any cuts agreed upon in a new treaty.
Russia's Foreign Ministry spokesman Andrei Nesterenko had earlier said Moscow was counting on resolving all the remaining questions in the very near future, if not in hours.
But Kremlin spokesman Natalia Timakova, who was traveling with Medvedev, later issued a highly unusual public rebuke to Nesterenko, telling reporters what he said has nothing in common with reality.
The differences in Moscow's position may reflect discrepancies between Medvedev and Prime Minister Vladimir Putin, Russia's pre-eminent politician and the country's ultimate decision-maker.
Putin, who is frequently critical of the United States, intervened in the summer to scupper a deal on Russia joining the World Trade Organization, only hours after senior U.S. and Russian officials said they were close to agreement.
A senior U.S. official had said in Washington on Thursday that Obama and Medvedev could reach an agreement in principle in Copenhagen on the arms treaty but this did not materialize.
Talks between the two sides have been conducted in Geneva under unusually tight secrecy, and very few details of the negotiations have come to light.
Tensions surfaced on Thursday when Russian Foreign Minister Sergei Lavrov, a longtime Putin loyalist, accused U.S. negotiators of dragging their feet -- a charge rebutted by Washington.
The START I treaty, signed in 1991 by U.S. President George Bush and Soviet leader Mikhail Gorbachev, took nearly a decade to achieve but resulted in Russia and the United States more than halving their nuclear arsenals.
Obama and Medvedev said in July they wanted a new treaty that would reduce operationally deployed nuclear warheads to 1,500-1,675, a cut of about a third from current levels.
They also agreed that strategic delivery systems -- the missiles, bombers and submarines that launch nuclear warheads -- should be limited to between 500 and 1,100 units.
Precise figures on deployed nuclear weapons are secret but the U.S.-based Bulletin of the Atomic Scientists estimated at the start of 2009 that the United States had about 2,200 operationally deployed nuclear warheads and Russia about 2,790.
(Writing by Michael Stott in Moscow; editing by Andrew Roche)