The Start treaty led to huge reductions in the Russian and US nuclear arsenals
Russia and the US have both said it should soon be possible to conclude a new nuclear disarmament treaty.
Officials in Moscow and Washington said US President Barack Obama and Russian President Dmitry Medvedev had a "good conversation" reviewing negotiations.
The two countries are trying to replace the 1991 Strategic Arms Reduction Treaty, which expired last December.
The US says it has more than 2,000 nuclear weapons, while Russia is believed to have nearly 3,000.
Secretary of State Hillary Clinton is to discuss nuclear disarmament with Russian Foreign Minister Sergei Lavrov later this week in Moscow.
In a telephone conversation on Saturday, the two presidents "expressed satisfaction with the high level of consensus on the basic lines" of the treaty negotiations, the Kremlin said in a statement.
The pair "stressed that it is already possible to set firm dates to submit the draft agreement to the heads of state for their signatures," the statement added, without setting the timeframe.
A spokesman for the White House National Security Council said: "Both leaders are committed to concluding an agreement soon."
US plans for a missile defence system in Eastern Europe have irked Russia
The two presidents launched talks to replace the Strategic Arms Reduction Treaty (Start) last April with an original deadline of December.
It was part of a Washington-inspired attempt to "reset" relations with Moscow after years of frayed ties under the administration of former US President George W Bush.
The landmark Start pact was signed in 1991 and led to huge reductions in the two countries' nuclear arsenals.
Both sides have agreed to cut the number of warheads they hold to between 1,500 and 1,675 each.
But there have been disagreements on verification measures, how to count weapons and launch systems.
Another bone of contention is the US plan for a missile defence system in Eastern Europe.
In their telephone call, the two leaders agreed to give their negotiators "additional instructions" for concluding a draft treaty, the Kremlin statement said.
US and Russian negotiators have been meeting in Geneva to discuss a successor to the Start treaty.
President Obama has said his goal is to have a nuclear-free world. He has promised to cut the number and role of nuclear weapons in US security strategy.
The US is hosting a nuclear non-proliferation summit in Washington in April.
All numbers are estimates because exact numbers are top secret.
Strategic nuclear warheads are designed to target cities, missile locations and military headquarters as part of a strategic plan.
Israeli authorities have never confirmed or denied the country has nuclear weapons.
The highly secretive state claims it has nuclear weapons, but there is no information in the public domain that proves this.
The International Atomic Energy Agency reported in 2003 there had been covert nuclear activity to make fissile material and continues to monitor Tehran's nuclear programme.
US officials have claimed it is covertly seeking nuclear weapons.