The death of al-Qaeda's leader in Iraq is a strike against the terrorist group everywhere, Tony Blair has said.
Abu Musab al-Zarqawi appeared in a video earlier this year
Mr Blair welcomed news of Abu Musab al-Zarqawi's death but said it would not stop people dying in Iraq.
Urging the world to unite on the Iraq issue, he told his monthly news conference: "If we defeat al-Qaeda in Iraq, we will defeat it everywhere."
The prime minister said Zarqawi had been a "hands-on" leader but others would try to continue his work.
Al-Qaeda in Iraq has been blamed for bombings which have killed hundreds of Shias and US troops.
And Zarqawi was personally suspected of being involved in the murder of Ken Bigley, a 62-year-old engineer from Liverpool, who was taken hostage in September 2004 and beheaded two weeks later.
Mr Bigley's brother Stan said: "I'm glad he's off the face of the earth, not just for my brother but for all the people he has killed."
'Have no illusions'
US military chiefs say Zarqawi was killed in an air raid near Baquba.
The head of US-led forces in Iraq, General George Casey, said his body was identified through fingerprints and facial recognition.
Mr Blair used his monthly news conference in Downing Street to hail both Zarqawi's death and the completion of the new Iraqi Government.
Zarqawi had been the most "vicious prosecutor" of attempts to wreck democracy in Iraq, he said.
"We should have no illusions. We know they will continue to kill, we know there are many, many obstacles to overcome," he said.
"But they also know that our determination to defeat them is total."
Mr Blair called for a change in the "mindset in Western opinion" which suggested that daily bloodshed in Iraq meant British and American troops should not be there.
The Iraqi people needed help to protect democracy and avoid sectarian conflict, he argued.
He said the new Iraqi government, headed by Prime Minister Nouri Maliki, had a "significantly different feel about it" and was "gripping things".
Tony Blair hailed Iraq's new government at his monthly briefing
Mr Maliki's decision to name his defence and interior ministers was a sign of "a new spirit to succeed", said Mr Blair.
"Our task, obviously, is to turn that spirit, that willingness, that desire to succeed into effective action," he said.
"If we are able to do so, then we will have accomplished something that goes far beyond the borders of Iraq."
Foreign Secretary Margaret Beckett agreed that "we're entering into a new phase of issues in Iraq, that there is an opportunity again for Iraq to move forward in a much more peaceful way.
"Let us hope that opportunity is taken because I'm sure that's what the majority of Iraqi people want, like people anywhere in the world."
She cited "the combination today of getting agreed nominations for important ministerial posts, of getting that endorsed by the elected council, and then also the removal of a powerful voice that was urging disorder, violence and so on."
Respect MP and anti-war campaigner George Galloway told BBC One's Question Time programme that the death of Zarqawi would not make a difference to the violence seen in Iraq.
The new Iraqi prime minister announced the death of Zarqawi
"It won't change a thing," he said.
"The United States deliberately built up this Zarqawi as a bogeyman to try and perpetrate the lie that the resistance in Iraq are foreigners who have come from elsewhere and that the mass of the Iraqis are with the American and British occupation.
"That was always a lie."
Lynne Featherstone, the Liberal Democrats' home affairs spokesman, added that she thought the death of Zarqawi could be "a false dawn".
"There is hope but not much because the actual breakdown of law and order is so much more severe than simply a single head of al-Qaeda," she said. "It is a multi-headed organisation and the UN needs to engage."
A fellow panellist, Conservative shadow defence secretary Dr Liam Fox, said a new government "gave the best hope" to Iraqis that they "now have a chance to live with the sort of democratic freedom and rule of law that some people in this country take for granted".