Soldiers combed the crash site for survivors
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Defence Secretary Donald Rumsfeld has vowed the United States will stay in Iraq until the battle is won, despite the loss of 18 US lives in one day.
"In a long hard war, we are going to have tragic days," Mr Rumsfeld said.
In the heaviest US losses since the height of the war, 15 soldiers were killed and 21 wounded when a Chinook helicopter was downed near Falluja.
The incident prompted two senior US senators to call on President Bush to send more troops to Iraq.
US military officials and witnesses said the giant aircraft had been shot down early on Sunday.
And in Falluja itself, a roadside bomb killed two American civilian contractors while another soldier was killed by a bomb in Baghdad.
The administration appears more and more sensitive about the effect of the casualties on public opinion at home, says the BBC's Justin Webb in Washington.
There has not been such loss of American life on one day in Iraq since 23 March - during the war to oust Saddam Hussein - when 28 soldiers were killed in various clashes, 18 of them in a single battle at Nasiriya.
Some Iraqis in Falluja - a centre of opposition to the US-led occupation - openly welcomed the American casualties.
"This was a new lesson from the resistance, a lesson to the greedy aggressors," one Iraqi told AP news agency in Falluja.
At the scene of the roadside bomb, Iraqis danced on the wreckage and one youth sported a US helmet.
Missile threat
Mr Rumsfeld said he accepted that troops faced a continuing risk of attack, including that of surface-to-air missiles (SAMs).
"We've known about surface-to-air missiles since before we went
in," he said.
"They are dangerous and they exist in that country in large numbers, as they do in that part of the world. So it's always a risk."
Hundreds of SAMs, mainly Russian-made, are said to be still scattered across Iraq despite a coalition campaign to collect them with a reward of $500 offered per missile.
Paul Bremer, the US civil administrator in Iraq, suggested on Sunday that the situation was "getting worse".
"We've seen a much more sophisticated use of improvised explosive devices against coalition forces," he said.
'Misled into war'
One of the leading contenders for the Democrat candidacy in next year's US presidential election, Wesley Clark, launched a stinging attack on the Bush administration's record in Iraq after Sunday's attacks.
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MAJOR POST-WAR ATTACKS
27 Oct: 36 killed in co-ordinated suicide attacks on Red Cross HQ and police stations in Baghdad
29 Aug: Shia Muslim cleric Ayatollah Mohammed Baqr al-Hakim among 80 killed in bombing in Najaf
19 Aug: UN special representative among 22 killed in attack on UN HQ in Baghdad
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"We were misled into this conflict without a real strategy for success," Mr Clark, a former commander of Nato, told the Associated Press.
Later Senate Foreign Relations Committee Chairman Richard Lugar, a Republican, and Joseph Biden, a senior Democrat on the committee, said numbers of troops might have to be increased and additional help sought from traditional but reluctant allies such as France and Germany.
"In the short term, we may need more American forces ...
and we have to be prepared to go back to our European friends
and say 'we need more help, we are willing to give you more
say'," Senator Biden told the CBS network.
The Pentagon has discouraged American news organisations from photographing the coffins of dead soldiers returning home.
There was also a reported attempt on Sunday by American troops to confiscate news footage from the scene of the helicopter crash.
Our Washington correspondent says the sensitivity of the administration is understandable because the White House is trying to persuade Americans that in most of Iraq the situation is improving and such imagery is unhelpful.
Meanwhile the US Senate, which is investigating US intelligence used to justify the war in Iraq, received a promise from the government on Sunday that it would be given all the files it had requested.