Tony Blair believes a UN resolution on providing humanitarian relief for the Iraqi people could be passed within 24 hours.
Blair wants UN endorsement for post-war plans
Mr Blair is flying back to London after a Camp David summit with US President George W Bush and discussions with Kofi Annan about the humanitarian situation in Iraq.
The prime minister and the UN secretary general welcomed the news that a draft UN resolution on re-starting the oil-for-food programme could be put to a vote soon, possibly later on Friday.
That would be the "UN door open again" - possibly making it easier to involve the UN in rebuilding and governing post-war Iraq, Mr Blair said in an interview for BBC Radio 4's Today programme.
UK ministers have said two new UN resolutions on Iraq are vital - one to re-start the oil-for-food programme and another to address rebuilding Iraq after the conflict.
But the Bush administration is thought to be sceptical about full-scale UN involvement in a future post-war administration in Iraq.
In the interview, Mr Blair also expressed satisfaction with how the first week of the war had progressed although he admitted there had been "tough and difficult moments".
"I do point out again we're a week into this and an awful lot has been achieved," he said.
"But you're not going to prise the grip of Saddam off the country when it's been there for over 20 years."
He added that the British public still had not fully grasped the "real" links between terrorist groups and rogue states in possession of weapons of mass destruction.
"We haven't really opened our eyes to it - but it is real," he told Today.
Mr Blair briefed Mr Annan on his earlier summit with President Bush at Camp David.
Earlier, he told a joint news conference "an enormous amount" had been achieved in the conflict so far, but it was not right to speculate about when the war would be over.
The prime minister's official spokesman described the Camp David talks as "a great success" and the mood as "friendly, constructive and open".
Mr Blair also accused Iraq of "executing" the two British soldiers whose bodies were shown on Arabic television station al-Jazeera - a claim Iraq denies.
He said: "If anyone needed any further evidence of the depravity of Saddam's regime,
this atrocity provides it."
Asked why he had referred to their deaths as executions, Mr Blair said it was "because of the circumstances we know".
The two British soldiers who went missing on Sunday, and are believed dead, have now been named as Sapper Luke Allsopp, 24, and Staff Sergeant Simon Cullingworth, 36, both from a bomb disposal unit of the Royal Engineers.
'Grip of terror'
Iraqi Information Minister Mohammad Saeed al-Sahaf later told Abu Dhabi television that Mr Blair had "lied to
the public" about the soldiers, adding: "We haven't executed
At the joint news conference with the prime minister, President Bush said the war would be "as long as it takes".
"Slowly but surely the grip of terror around the throats of the Iraqi people is being loosened," he said.
As Mr Blair began his meeting with Mr Annan, the spokesman added he was confident the UN would approve the oil-for-food programme without delay.
The prime minister has said the UN will be important in shaping Iraq's future.
Sir Jeremy Greenstock, British ambassador at the UN, said UK wanted the UN to play a "central role in the future of Iraq".
But President Bush has given no commitment to backing an interim UN-led administration in Iraq in the future.
He said: "Iraq's greatest long-term need is a representative government that protects
the rights of all Iraqis.
"The form of this government will be chosen by the Iraqi people, not imposed
Mr Blair says detailed discussions are needed and that it would be premature to decide on a post-war administration now.