The American Under-Secretary of State for arms control, John Bolton, is meeting Russian Foreign Minister Igor Ivanov as the US lobbies other permanent members of the UN Security Council to back its campaign to disarm Iraq.
Chief UN weapons inspector Hans Blix is scheduled to visit Moscow on Tuesday for talks with Mr Ivanov.
The US Secretary of State, Colin Powell, has said Washington expects to present a draft resolution to the Security Council early this week aimed at forcing Iraq to disarm.
He said the resolution would impose a new tough weapons inspection regime with what he called "consequences" for Iraq if it did not comply.
It will no longer have an explicit authorisation for the use of force if Iraq blocks weapons inspections.
The resolution has been held up by disagreement between the US and France, which wants to ensure the Americans cannot automatically use force against Iraq on the basis of a single resolution.
Russia says the sole objective of a new UN resolution should be to ensure the rapid return of weapons inspectors.
In another development, the head of the International Atomic Energy Agency, Dr Mohamed al-Baradei, told the BBC he was confident Iraq would agree to allow inspectors to visit any site they choose when they return to Baghdad.
"I think the understanding that Iraq now has is that we will not leave any stones unturned," he said.
He said successful weapons inspections relied on:
A BBC correspondent at the UN says that while the Americans have toned down some of their original language in the draft resolution, France has still not been won over.
President Jacques Chirac, fresh from a summit of Francophone nations in Beirut, said on Sunday that a "very large majority" of countries shared the French position that the new resolution should not explicitly authorise an attack on Baghdad.
Tough debates
Mr Powell made it clear that Washington firmly rejected the French demand that the Security Council must pass a further resolution before anyone could go to war.
However, he conceded that tough debates on the issue lay ahead.
Iraq insists there is no need for a new UN Security Council resolution and accuses weapons inspectors of breaking existing rules before their withdrawal from Iraq in 1998.
Mr Blix has said that weapons inspectors are ready to start work in Iraq within 10 days of the Security Council adopting a new resolution.
US President George W Bush and Russian President Vladimir Putin are expected to discuss the Iraq situation when they meet on the sidelines of the Asia Pacific Economic summit in Mexico later this week.