Tony Blair has vowed the government will stand firm in its "historic struggle" against Iraqi insurgents.
Blair repeated his backing for UK's role
Writing in the Observer, the prime minister said if the coalition failed, "the hope of freedom and religious tolerance would be snuffed out".
He denied a civil war was already under way, and blamed the violence on supporters of Saddam Hussein.
Mr Blair, who is holidaying in Bermuda, said he fully backed the US handling of the situation.
He condemned a "significant part" of Western opinion which opposes the war and is sitting back "replete with schadenfreude at the difficulties we find".
Failure by the coalition would mean "dictators would rejoice, fanatics and terrorists would be triumphant".
Cost of failure
Mr Blair dismissed those attacking coalition forces as former supporters of Saddam Hussein, al-Qaeda-backed terrorist groups or followers of the radical cleric, Moqtada Sadr.
He said that much of Iraq was unaffected by the uprising, and that many Iraqis were against it.
"We are locked in an historic struggle in Iraq. Were we to fail, which we shall not, it is more than the 'power of America' that would be defeated," Mr Blair said.
"The hope of freedom and religious tolerance would be snuffed out."
On Sunday, Defence Secretary Geoff Hoon told the BBC the coalition would "continue to operate together", and he said he was prepared to send more British troops to Iraq "should that become necessary", but that the situation around Basra was calm.
"The Iraqis in the south are supportive of the British presence, of the presence of coalition forces. They know we are there to help restore sovereignty to their country and allow for rebuilding and reconstruction.
"That message is the case right across Iraq with the exception of those places like Falluja where we have seen men of violence trying to kill Iraqis just as much as they have been trying to kill coalition forces.
"We can't simply sit back and allow people to be killed. That threat to security has to be dealt with," he said.
Conservative opposition leader Michael Howard echoed the former Foreign Secretary Lord Hurd, who called for a special envoy to be sent to Baghdad to make sure the UK has a greater say in decision-making.
"At the very time our voice should be stronger it's been weakened," he told BBC News 24.
"We've been punching above our weight militarily, but below our weight politically and diplomatically.
"We need someone who should be Paul Bremer's deputy (the US administrator in Iraq). It is important that we have someone there with the necessary experience and seniority in the decisions that are taken.
"After all we have the second largest military contingent and were with the Americans from the outset."
After days of fighting, the US has reported the deaths of at least 42 of its soldiers in combat since Sunday.
The US forces are now fighting Sunni and Shia militants in different parts of the country.
In Falluja, there has been six days of fighting between Sunni militants and US forces.
An Iraqi civil defence base some 10km south of al-Amara in the south-east of the country, where some 25 British troops are involved in training operations, came under attack on Saturday evening.
A spokesman for the Ministry of Defence denied reports of casualties on al-Jazeera news and said nine mortar rounds had been fired, but had caused neither injury nor damage.
Former Foreign Secretary Robin Cook told the BBC that the US had "achieved the impossible".
"Last year we were worried that the Sunni and Shia might fight each other. By attacking both together, Paul Bremer has convinced them that they have a common enemy in the United States," he said.
"The British troops have defused tension. If the Americans had we wouldn't be in the position we are now.
"The worrying thing is that there has to be a danger that the behaviour of the US forces will spill over into the British sector and we will be regarded as fair game as part of the occupation forces."