Tony Blair has said Britain, too, is "at war with terrorism" and predicted President Bush will secure a worldwide coalition to hunt down those responsible for Tuesday's atrocities against America.
With as many as 300 Britons now feared dead, the Prime Minister again said the British and American interest was joined, and signalled the United Kingdom would play its full part in the action being planned by the President and his advisers.
"This is a time for a calm head and cool nerves," he told CNN. "We will see this through. It will be done."
Echoing the American President's declaration of "war" for the first time, Mr Blair told his interviewer: "Yes. Whatever the technical or legal issues about a declaration of war, the fact is we are at war with terrorism."
Confirming that the British death toll would be the highest ever in a terrorist attack, the prime minister said: "Probably 200 to 300 people from Britain will have died. That makes it the worst terrorist attack there has been on British citizens since the second World War."
Praising President Bush for his handling of the crisis, Mr Blair said: "I am very pleased at the way the American administration has gone out of its way to consult its allies. There has to be a response to bring those terrorists who committed this act to account and we will play our full part in that."
The prime minister continued: "Secondly there has to be an agenda we construct at international level to dismantle the machinery of international terrorism."
Making clear he would not flinch from supporting military action, Mr Blair said: "We have made it clear that we stand side by side with the United States," adding: "It's right that when we merely offer words of support, that's the easy part in one sense. The hard part starts when we actually take the action, but I think that support will be there."
The newly-elected Conservative leader, Mr Iain Duncan Smith, again strongly backed the British Government's stance and said Mr Blair had a vital leadership role in the unfolding crisis.
However, the leader of the Liberal Democrats, Mr Charles Kennedy, sounded a note of caution, suggesting that support for the United States did not amount to "a blank cheque" for any kind of military action.
Speaking on GMTV's Sunday programme, Mr Kennedy said: "President Bush has not responded in an instinctive, knee-jerk way and I think people like Colin Powell and so on, who are vastly experienced, are people that we look to with some trust and some confidence. But that doesn't mean a blank cheque."
Mr Kennedy continued: "We have got to have a measured response, when that response comes we have got to be clear. Who is it and where is it need to be the focus of any military response, and we need to continue to question, in the democratic sense, all the decisions that are arrived at without compromising national or international security."
Mr Duncan Smith, speaking on the BBC's Breakfast with Frost programme, insisted there should not be "a glimmer of light" between Britain and the US. "It's critical we show the rest of the world we won't be parted from them, we won't allow a glimmer of daylight between us. That's the leadership role the Prime Minister must play."
And the leader of the Commons, Mr Robin Cook, said "nothing is ruled out and nothing is ruled in" in considering whatever specific requests for assistance were made by the Americans. "This is not something that is going to be resolved by one quick magic strike. It's going to take determination, it's going to take time," he warned.
The Foreign Secretary, Mr Jack Straw, confirmed the government would pay for relatives of the victims of the attack on the World Trade Centre to visit New York, and that his officials were working hard to arrange flights as quickly as possible.
"Because of our close contact with the families, we know and understand how keen many of the families are to get to New York. We are moving as fast as we can to make this happen," he said. More than 20,000 Britons have contacted helplines in the desperate bid to contact missing relatives and friends.
When they arrive in New York, British families will have the support of 30 consular staff, 20 British police officers and 10 counsellors.