Tony Blair has said he is confident agreement can be forged at the United Nations on the administration of a post-Saddam Iraq.
Blair wants UN endorsement for post-war plans
The prime minister told the BBC that the US was in full support of UN involvement after the war.
Mr Blair also said he did not know whether Saddam Hussein was alive or dead - but insisted that the Iraqi people were "desperate" to see the end of Saddam's "brutal regime".
He said Iraqis would not "rise up" until they knew the "thin, but strong membrane" around the Iraqi leader had been destroyed.
Mr Blair, who refused to speculate on how long military action would take, said he had always expected "tough and difficult moments" in the conflict but insisted that "an awful lot has been achieved".
In respect of post-Saddam Iraq, everyone agrees it would be best to have a UN resolution governing this situation
Mr Blair hopes a UN draft resolution on the oil-for-food programme for Iraq could be put to a vote on Friday and as a "door opening" to greater international agreement.
Tabled by Germany, the draft resolution has also seen the diplomatic row between the UK and France put to one side as they are co-sponsors along with Chile and Bulgaria.
Mr Blair was speaking at the end of a trip to the US which included a Camp David summit with US President George Bush and an hour-long discussion with UN Secretary General Kofi Annan in New York.
Speaking to BBC Radio 4's Today programme before flying back to London, Mr Blair said it was hoped a UN vote on reviving the oil-for-food programme could take place on Friday.
The programme allows Iraq to sell oil to buy food and medicines, providing a lifeline for 60% of Iraqis, but was suspended last week.
It was run jointly by the UN and the Iraqi government.
The new resolution would transfer authority for the administration of the programme to Mr Annan.
Hoping the vote could signal a new phase of international co-operation, the prime minister added: "That will be the UN door opening again."
UK ministers want two new UN resolutions on Iraq - the first to revive the oil-for-food programme and a second to map out the reconstruction and administration of post-war Iraq.
And Mr Blair denied reports of divisions with the US about the make-up of post-war Iraq and said: "Everybody wants any post-Saddam regime to be as broad-based as possible and to have the endorsement of the UN."
"That is why we agreed - myself and President Bush, Prime Minister Aznar at
the summit that we had in the Azores - that not just the humanitarian element
but also the civil administration in Iraq should be governed by UN resolution."
Despite failing to establish agreement for a second UN resolution before going to war, Mr Blair said there would be no repeat of this situation.
And speculation that Washington was keen to sideline the UN in administrating Iraq was untrue, he added.
"I can absolutely assure you from the conversations I've had with him (Mr Bush) that his priority is to make sure the government of Iraq after Saddam is as broadly represented as possible," he said.
Earlier, at Camp David, the president gave no commitment to backing an interim UN-led administration in Iraq in the future.
The prime minister told Today the detail of the UN's involvement had yet to be worked out, because the priority was the war itself.
Mr Blair admitted there was a reluctance by the Iraqis to rebel against Saddam because they had been let down by the coalition in 1991.
But he added: "They are going to wait and watch and see what happened but do not be in any doubt at all - the Iraqis are desperate for Saddam to go."
Mr Blair said he believed the UK had not "opened our eyes" to the "new security threat" posed by terrorism.
"I think America has, in a sense, because of September 11, because it was
such a gross atrocity that it shook and changed its entire psychology," he said.
"But the security threat is real. The link between these rogue aggressive
states with weapons of mass destruction and terrorist groups - those links are
Later, Labour MP Bruce George, chairman of the Commons defence committee said it seemed the strategy over Iraq was "creaking".
He told BBC Radio Five Live there were not enough troops to achieve the objectives at present, which is why more were being drafted in.
He said the plans were being "restructured" by the US and UK governments - and that the march on Baghdad may be being delayed as a result.