White House spokesman Ari Fleischer said the UN had a limited time to agree to the US and UK-backed proposals that would force Iraq to comply with weapons inspections or face military action.
And President George W Bush, campaigning for Tuesday's mid-term congressional elections, said: "If the United Nations can't make its mind up, if [Iraqi President] Saddam Hussein won't disarm, we will lead a coalition to disarm him for the sake of peace."
The Americans circulated the new draft resolution to Security Council members on Monday.
It was drawn up after an earlier text, which explicitly threatened military force against Iraq, was rejected by France, Russia and China - all of them, along with the US and UK, permanent members of the Security Council.
Details of draft resolution
The BBC's David Bamford, at the UN, says details of the new draft resolution have begun to emerge.
Although the Americans have made a slight concession, he says, there is still no mention of any US obligation to seek Security Council approval for military action against Iraq.
The revised text declares Iraq to still be in breach of UN resolutions on weapons inspections, and demands a full list of Iraq's weapons programmes within a month of the resolution being passed.
Saddam Hussein would also have to provide UN weapons inspectors with immediate, unimpeded, unconditional and unrestricted access to anything they wanted to investigate.
The new draft resolution drops an earlier reference to the use of "all necessary means" - a phrase understood to mean military force - if Iraq does not meet its obligations.
Instead it allows - but does not require - the Security Council to consider using force if and when the UN weapons inspectors report that Baghdad is blocking their work.
'Much work to do'
Ambassadors from the five permanent members of the UN Security Council wound up a second day of talks in New York on Tuesday without resolving their differences.
Russian Foreign Minister Igor Ivanov said the new draft resolution did not meet Moscow's criteria and was unacceptable.
"The US resolution project which was presented yesterday so far does not correspond to the criteria (for a settlement of the Iraqi crisis) which Russia has put forward and by which it stands," he was quoted by the Interfax news agency as saying.
He said he was ready to work with all members of the Security Council to find a solution, but he said that solution should exclude any possibility of an automatic use of force against Iraq.
Mr Ivanov's French counterpart, Dominique de Villepin, said a lot of discussion would be required before agreement could be found.
"Some progress is still needed and we therefore still have much work to do," he said.
Their comments came as the chief United Nations weapons inspector, Hans Blix, met Mr Ivanov in Moscow to discuss efforts to send weapons inspectors back to Iraq.
France and Russia have been pushing for a two-step approach at the United Nations, in which a first resolution would set out new guidelines for weapons inspections.
A second would allow for force to be considered only if Iraq was deemed to have violated the first resolution.