The death toll of US soldiers in Iraq reached 4,000 yesterday, days after the fifth anniversary of a war that President George W. Bush says the US is on track to win.

The US military said four soldiers were killed on Sunday when a roadside bomb, the biggest killer of American soldiers in Iraq, exploded near their vehicle in southern Baghdad.

One soldier was wounded in the attack, which brought the number of US military deaths to 4,000 since the US-led invasion in 2003.

The deaths came on a day when the US-protected "Green Zone", the government and diplomatic compound in central Baghdad, was hit by repeated rocket and mortar fire, part of an upsurge in violence in the capital and elsewhere.

Sunday's violence, in which dozens were killed, underscored the fragility of Iraq's security. There has been an increase in attacks since January, although US military commanders say overall levels of violence are down 60 per cent since last June.

What impact the 4,000 milestone will have on a war-weary American public and the US presidential campaign will be hard to assess in the short term, but war critics are likely to seize on it to boost their case for US troops to be withdrawn.

"You regret every casualty, every loss," US Vice President Dick Cheney said during a visit to Jerusalem. "It may have a psychological effect on the public, but it's a tragedy that we live in a kind of world where that happens."

The US military dismisses such tolls as arbitrary markers.

"No casualty is more or less significant than another; each soldier, marine, airman and sailor is equally precious and their loss equally tragic," US military spokesman Rear Admiral Greg Smith said yesterday.

Anthony Cordesman, a respected Iraq analyst at the Centre for Strategic and International Studies in Washington, said the 4,000th death could trigger another wave of polarised debate.

"Those who oppose the war will see it as further reason to end it. Those who support it will point to military progress and say that future casualties will be much lower," he said.

Although Americans are more preoccupied with domestic economic troubles, the Iraq war is still an important issue in the presidential campaign, with Democratic hopefuls Hillary Clinton and Barack Obama calling for a timetable for withdrawal.

Mr Bush said in a speech marking the fifth anniversary of the war on March 19 that the US was on track for victory and said withdrawing troops, who now number about 160,000, would embolden al Qaeda and neighbouring Iran.

He said he had no regrets about the war, which has pushed his approval ratings near the lowest level of his presidency, but acknowledged the "high cost in lives and treasure".

Mr Bush launched the war in March 2003 hoping for a quick victory with minimal casualties. The Iraqi army was quickly defeated, but within months insurgent attacks had bogged down US forces who struggled to develop a strategy to defeat them.

The 1,000th US soldier to die was in September 2004, 18 months after the invasion and in the midst of a presidential election that returned Mr Bush to office for a second term.

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