The Prime Minister's remarks were seen as a call to the Iraqi people to help the Allies overthrow President Saddam.
There were also growing signals that the action could be sustained in an attempt to destabilise the Iraqi leader. Mr Blair's official spokesmandescribed the bombings as "significant action", comparable to the first strikes on Iraq in the Gulf War.
Mr Blair, who was deploying British forces for the first time since taking office, confirmed that Operation Desert Fox was going ahead as the first strikes began. "Our quarrel is not with the Iraqi people," he said. "It never has been ... Our quarrel is with him [Saddam] alone.
"There is no realistic alternative to military force. We are taking military action with real regret but also with real determination. We have exhausted all other avenues. We act because we must."
The Foreign Secretary, Robin Cook, had been hosting a Christmas party at the Foreign Office as the attacks began. He told guests: "The phone calls will begin very soon."
Mr Blair, with the Downing Street Christmas tree behind him, said the action could have been avoided if President Saddam had kept his promises.
"The targets chosen are connected with his military capability, his weapons of mass destruction and his ability to threaten his neighbours. We are taking every possible care to avoid civilian casualties." The Prime Minister will make a statement to the Commons today.
The Tory leader, William Hague, pledged the support of the Opposition. "We pay tribute to the courage and outstanding skill of our armed services," he said. "We unite behind this action and the brave men and women of our armed services who have carried it out."
Most Labour MPs appeared ready to back the action after being told by the Prime Minister that the assurances given by President Saddam had been broken. But some backbenchMPs attacked Tony Blair for "slavishly" following President Bill Clinton's policy.
George Galloway MP, who was planning to organise a vigil outside Number 10 once the bombing had started, said: "Clinton, already condemned as a liar, cheat and deceiver, has no compunction about seeking to save his own skin with the blood of innocent men and women and children in Iraq."
One backbencher said the decision was "disgusting" and claimed that the lives of thousands of Iraqi civilians were at risk. Another said he was appalled that many of his colleagues were joking and laughing as if nothing had happened.
"It's like... `Springtime for Hitler' [a song in the film The Producers]. The Parliamentary Labour Party has turned into a chorus line for Tony Blair and Bill Clinton. It's just so obviously a cynical move by Clinton to ensure the heat is taken off him at home," he said.