Tony Blair appeared relaxed as he took to the lecturn for his monthly press briefing in Downing Street.
He opened by drawing attention to pleasing new figures on dealing with asylum claimants.
Andrew Marr for the BBC
The Iraqi Governing Council has announced that the draft UN resolution is "below expectations". What are your thoughts on this and how long will British troops be there?
Mr Blair believed the actual statement from the Council to be more positive: "welcomed as a sound basis" for getting a resolution.
He said the UK must remain in Iraq until the job is done and that achieving a democratic and stable Iraq is a good thing.
The timing of withdrawal depends on the ability of the Iraqi Government to assure security. But the Iraqi Government will have full sovereignty after 30 June.
Nick Robinson for ITN
Will UK forces be out in months not years? And will the Iraqi Government have a veto on military action they disapprove of?
The basic position is troops should only remain as long as it is necessary for them to effect a stable transition.
The issue is how fast can Iraq develop an indigenous security service?
After 30 June there will be a full transition of sovereignty. It will be up to the new governing body to decide how long foreign forces remain.
Mr Blair explained: "The idea is to engage in a transition where the Iraqi capability increases and ours reduces," and "that transfer of sovereignty is a real transfer."
Andy Bell for BBC Five Live
Will the Iraqi Government be able to veto a Fallujah-like attack?
Mr Blair said they would and similar attacks would have to be done with the consent of the Iraqi Government.
Elinor Goodman for Channel 4
Given that no WMDs have been found do you worry that you have been duped by Chalabi and the Iranians? Do you worry that the electorate might use 10 June as a protest vote on Iraq?
Mr Blair said local services matter and the European elections matter in their own right.
He said he had always believed in WMD and the conundrum will be solved in due course.
And he described Iraq as "not a benign place", with the visible degradation of 60% of the people on food aid; mass graves.
The PM recognised the "hard times" the coaltion countries had been through but he does foresee a "path forward".
Robin Oakley for CNN
Geoff Hoon said the decision to send more troops had not yet been taken so where is the pressure to send more troops coming from -commanders on the ground or from Bush?
If more troops went to Iraq they would operate as they do now, under a coalition banner, under British command.
He said no decision on further troops has been taken, but the UK would review the best way to fulfil our obligations.
For RTE news
Do you still believe that WMDs will be found?
Mr Blair said: "We know that he had them". He said Saddam Hussein used them against his own people and during the Iran/Iraq War.
The PM also acknowledged that WMDs haven't been found in Iraq yet, but that will be resolved.
The resolution made in Bush's speech will need international cooperation. Will he get international backing for the resolution?
The US is putting $20bn dollars into Iraq, Mr Blair advised and that fact should not be ignored in international opinion.
Middle East News
None of the Governing Council trust the Interim Government and they wonder what might happen to them after the coalition withdrawal. No attention is being given to training civil society.
Mr Blair claimed a huge process to convert Iraq to democracy is possible but what happens to individual members of the Iraq Council is best left to the UN.
He gave the examples of trying to help civil society working with civil rights groups and women's groups.
Will you be announcing a timetable for troop withdrawal? Won't this be difficult if they are under the control of the new Iraqi Government?
Mr Blair explained that UK troops cannot be ordered about as such, even under the coalition.
He said he didn't know whether the timetable would spell out specific dates but would be determined by the success of the mission.
If the Iraqi Government has a veto power would the US accept this too?
The PM reiterated that a transfer of sovereignty is a transfer of sovereignty and that troops will remain with the consent of the Iraqi Government.
Will there be a massive boost of troops in order to ensure security?
Mr Blair said what needs to happen is for Iraqi capability to be built up and the coalition is working with the provisional Iraqi Government to do that.
He spoke of a propaganda campaign saying that the coalition wants to occupy and steal oil but that these elements are stopping the country from forming a democratic government.
Will you put Scottish voter's minds at rest about the Tories and the return of the Poll Tax?
The PM said he was not surprised that the Tories are stuck in 1997.
Mark Mardell for the BBC
Do you think the Abu Ghraib pictures reflect a badly behaved military culture encouraged by politicians?
Mr Blair blamed the wrong actions of the individuals and said he didn't know of any US politicians who don't condemn these actions.
Adam Boulton for Sky News
On your future, isn't it better to tell people that you might want to go mid-term?
The PM said he had nothing more to add to what he'd said before.
Abu Ghraib is also a symbol of Saddam and could be made into a museum rather than destroyed. Is the US aiming to have the biggest Embassy in the world plus army bases in Iraq?
Mr Blair emphasised the Iraqis would decide for themselves.
He recalled the purpose of the action in Iraq was to liberate the country from Saddam Hussein.
Now that the country is liberated it's a question of helping Iraq to be run by Iraqis for Iraqis and the relationship with US is up to the new government.
Zapatero has insisted that the war was based on lies. What will your relationship be with him?
We disagree on Iraq. I have no doubt that our relationship will continue.
What about the British presence in Iraq after 30 June - will there be a British Embassy in Baghdad and an office in Kircuk? And what about the recognition of Kurdistan?
He said the UK has consular offices dotted around various countries and there is no hidden agenda.
Are you concerned the Bank of England has said that it isn't its job to stop the housing market from busting?
The PM said it was their job to sort out inflation and interest rates.
George Jones, The Daily Telegraph
If you felt you were a liability you've said you would stand down. How would you test being a liability?
The PM referred to his earlier answer on his future.
Patrick O'Flynn, Daily Express
On petrol prices 80p a litre was a psychological barrier during the last protest. Isn't it disingenuous to say that oil prices affect petrol prices when most of it is taken up in taxes?
No prices are going up is because of the international situation, especially with increased demands from China and US.
You can watch Tony Blair's May press conference on BBC Parliament from 2130 BST