Iraqi Deputy Prime Minister Tariq Aziz said Baghdad's pledge to readmit weapons inspectors had removed any justification for a US-led attack.
Russia agreed, saying that the threat of war had been averted and no further UN resolutions would be needed.
But America has dismissed the offer as a cynical ploy. Britain is backing the US, with Foreign Secretary Jack Straw insisting a new UN resolution on Iraq is still necessary.
The US administration wants a resolution that will allow the use of force against President Saddam Hussein if Iraq refuses to comply.
Mr Straw said the Iraqi offer was "bound to be treated with a high degree of international scepticism"
"We shall continue to work with our international partners for an effective resolution before the security council," the foreign secretary said.
'War averted'
The contrast with Russian reaction to Iraq's offer was stark.
"Thanks to our joint efforts, we managed to avert the threat of a war scenario and go back to political means of solving the Iraqi problem," Foreign Minister Igor Ivanov said.
"It is essential in the coming days to resolve the issue of the inspectors' return. For this, no new [Security Council] resolutions are needed."
The US, Britain and Russia are all permanent members of the United Nations Security Council wielding the power of veto.
The other two members are China, which welcomed the offer, and France, which said the council "must hold Saddam Hussein to his word".
The Security Council had been expected to discuss the Iraq issue soon, but those talks may now be delayed until later this week.
It is now understood that Russia wants discussion of the Iraq issue to wait until after bilateral meetings with the US in Washington on Thursday.
Iraq's Mr Aziz said: "All the reasons for an attack have been eliminated.
"They thought Iraq wouldn't take such a courageous decision."
Unconditional offer
Mr Aziz said the US was bent on war with Iraq, and that its true motive was hunger for Iraqi oil.
Meanwhile, the official Iraqi News Agency (INA) is reporting that Saddam Hussein will send a letter to the UN General Assembly in the next few days.
Key US air bases:
UN Secretary-General Kofi Annan received the unconditional Iraqi offer on Monday night, in a letter from Iraqi Foreign Minister Naji Sabri.
Iraq was ready to discuss the practical arrangements for the return of inspectors, Mr Annan said.
He added that he would pass the letter on to the Security Council "and they will have to decide what they do next".
The UN Secretary General said the inspectors in the UN Monitoring, Verification and Inspection Commission (Unmovic), and their chairman Hans Blix were "ready to continue their work".
An Unmovic spokesman told BBC News Online that the next step would be to resolve practical issues with the Iraqis, at talks in New York, before inspectors started moving in to Baghdad.
"We are ready to discuss practical measures, such as helicopters, hotels, the installation of monitoring equipment and so on, which need to be put in place," said Ewen Buchanan.
"We will not be dragging our feet. We have been ready to talk to them for some time."
Only after the satisfactory conclusion of these talks would inspectors and their back-up staff start moving in to Baghdad, he said.
Mr Annan paid "particular tribute" to all the states of the Arab League who played a "key role" in the Iraqi offer.
The Iraqis said they had made the decision in order to remove any doubts that they still possessed weapons of mass destruction.
They also said that their decision was a response to a speech from Mr Annan in which he said the admission of inspectors should be the first step leading to the eventual lifting of sanctions.
Deadline sought
US Secretary of State Colin Powell is still trying to get backing for a UN resolution giving Iraq a deadline on weapons inspections.
The US called Iraq's offer a "tactical step" to head off a resolution before it could be finalised.
"This is not a matter of inspection," said a White House spokesman.
"It is about disarmament of Iraq's weapons of mass destruction and the Iraqi regime's compliance with all other Security Council resolutions."
Meanwhile, the US is continuing to shift military hardware close to Iraq.
UN inspectors left Iraq four years ago after complaining of obstruction from the Iraqi authorities.
Since then, Iraq has refused to allow inspectors to return.