The United States and Britain have insisted they will not pull out of Iraq, despite attacks on their troops.
Troops have been ambushed regularly
On a visit to Iraq, UK Foreign Secretary Jack Straw said the incidents had increased London's and Washington's determination to root out remnants of Saddam Hussein's regime and his Baath party.
Mr Straw's comments echoed US President George W Bush's pledge on Tuesday to meet attacks with "direct and decisive force".
Six American soldiers were wounded on Tuesday in two separate attacks in the Iraqi capital, Baghdad.
At least 18 US soldiers have died as a result of hostile fire since 1 May, when President Bush declared major operations in Iraq over. Six British soldiers were killed last month.
BBC Washington correspondent Justin Webb says senior politicians of the main US political parties have been pressing the White House to be clearer about the nature of the commitment the US is going to have to make if Iraq is to be put on the road towards democracy.
The pressure comes as opinion polls show a marked decline in the number of Americans who are convinced of the success of the Iraq campaign.
The latest - carried out by USA Today, CNN and Gallup - found that 56% of respondents thought things were going well for US forces in Iraq - a drop from 70% a month ago and 86% in the second week in May.
The UK foreign secretary earlier visited the southern city of Basra - which is under UK control - a day after a ceremony for the Royal military policemen killed in Al Majar al-Kabir.
But he said the attack was a "relatively isolated" incident and vowed British forces would continue to hunt for the soldiers' killers.
The attacks were also being carried out by "petty and serious criminals" let out by Saddam Hussein's regime before the US-led military action began, Mr Straw said in Baghdad.
But coalition troops, he said, would deal with such attacks and establish the basis for representative democracy.
At a military swearing-in ceremony on Tuesday, Mr Bush talked of the massive and long-term undertaking that would be necessary in Iraq.
Previously he has stressed that the 230,000 US troops would not stay in Iraq a moment longer than was necessary.
"As commander-in-chief, I assure them we will stay on the offensive against the enemy. And all who attack our troops will be met with direct and decisive force."
The chief US administrator in Iraq, Paul Bremer, has dismissed recent attacks as the predictable and increasingly desperate response of the ousted regime.
Although the attacks appeared to have been co-ordinated locally, there was no evidence they were part of a centrally-controlled campaign, he said.
The new US-UK pledge comes amid controversy over what caused a huge explosion that killed lat least nine people at a mosque in the town of Fallujah, including the imam.
US military authorities say a bomb-making class triggered the explosion
The US statement said the class was being held inside the mosque.
Local residents had accused the Americans of causing the blast with a missile.