US Secretary of State Hillary Clinton says there has been "substantial" progress on a new nuclear disarmament deal with Russia.
In Moscow, Mrs Clinton and Russian counterpart Sergei Lavrov said a new Strategic Arms Reduction Treaty (Start) should be finalised soon.
The nations are trying to replace the 1991 Start that expired in December.
Mrs Clinton is attending two days of talks in Moscow, including a key meeting on the Middle East on Friday.
Iran is also a major issue, with the US and Russia publicly disagreeing on the planned opening of an Iranian nuclear power station.
Quartet meeting
Russian Foreign Minister Mr Lavrov said at a joint press conference with Mrs Clinton that Moscow and Washington were in the final stage of a new Start.
Mrs Clinton said: "The results of the latest negotiation rounds lead us to believe we'll be reaching a final agreement soon."
The US is said to have more than 2,000 nuclear weapons, while Russia is believed to have nearly 3,000. Both sides have agreed to cut the number of warheads they hold to between 1,500 and 1,675 each.
The US and Russia have disagreed on verification measures
But there have been disagreements on verification measures, how to count weapons and launch systems.
Mrs Clinton said in the past year the US and Russia had worked hard to "reset" damaged bilateral relations.
The BBC's Rupert Wingfield-Hayes in Moscow says that although no date was given, it looks likely the new Start will be signed before President Barack Obama hosts a big nuclear disarmament conference in April.
Our correspondent says relations between Russia and the US are much better than a year ago, but Mr Obama still has little concrete to show from the "reset" policy and badly needs the new treaty.
Mrs Clinton arrived in Moscow on Wednesday for talks on Thursday and Friday.