* U.S. death toll reaches 4,000
* Impact on U.S. election unclear
* Mehdi Army militia starts protest (Adds militia starts protest in Baghdad)
By Ross Colvin
BAGHDAD, March 24 (Reuters) - Four U.S. soldiers were blown up in Baghdad, pushing the U.S. military death toll in Iraq to 4,000 just days into the sixth year of a war that President George W. Bush says the United States is on track to win.
The U.S. military said on Monday the soldiers were killed on Sunday when a roadside bomb, the biggest killer of U.S. soldiers in Iraq since the 2003 invasion, exploded near their vehicle in southern Baghdad. One soldier was wounded.
On the same day dozens of Iraqis were killed in rocket and mortar attacks on the U.S.-protected "Green Zone" government and diplomatic compound in central Baghdad, and in other bombings in the capital and elsewhere.
What impact the 4,000 milestone might have on a war-weary American public and the U.S. 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hard to assess in the short term, but war critics are likely to seize on it to boost their case for U.S. troops to be withdrawn.
The White House said President George W. Bush was saddened by the loss of 4,000 troops and would focus on ensuring the United States succeeds in the five-year-old conflict.
"It’s a sober moment, and one that all of us can focus on," a White House spokeswoman said.
"The president feels each and every one of the deaths very strongly and he grieves for their families," she said.
The United States lost 58,000 troops in over a decade of fighting in Vietnam until 1975, and 54,000 in the three-year-long Korean war that began in 1950.
The U.S. military played down the latest Iraqi toll, saying it was an arbitrary marker.
"No casualty is more or less significant than another; each soldier, marine, airman and sailor is equally precious and their loss equally tragic," a spokesman said.
Anthony Cordesman, a respected Iraq analyst at the Center 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.
Cordesman criticised the media for focusing on the death toll when the number of wounded was "far, far higher and has more lasting impact as a human tragedy and in terms of costs".
Some 29,000 U.S. troops have been wounded in the war that has killed tens of thousands of Iraqis, as well as 175 British troops and 134 from other U.S. allies.
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.
Bush said in a speech marking the fifth anniversary of the war on March 19 that the United States 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".
The 1,000th U.S. soldier to die was in September 2004, 18 months after the invasion and in the midst of a presidential election that returned Bush to office for a second term.
The toll climbed to 2,000 in October 2005 as Sunni Arab insurgents battled to oust the Baghdad government, and 3,000 in December 2006, before Bush unveiled a plan to send 30,000 more troops to Iraq to quell the violence.
"I doubt the 4,000 milestone will have the impact that the 3,000 did. The conventional wisdom then was that things were going badly," said Stephen Biddle, a senior fellow for defence policy at the Council on Foreign Relations in Washington.
"Today, by contrast, the public’s general perception of Iraq is less negative, and coverage for the last six months has tended to focus on the reduction in violence and U.S. casualties. The war has also been much less visible," he said.
But the weekend barrages on the Green Zone, which houses the U.S. embassy, and the continued attacks on U.S. troops may indicate that Iraqi militants are trying to change that.
"Al Qaeda and extreme elements of the (Mehdi Army) have every incentive to find ways to raise the U.S. casualties between now and November and will be seeking ways to use bombings to raise the rate and number," Cordesman said.
Fighters from the Mehdi Army militia, which the U.S. military once called the greatest threat to peace in Iraq, ordered shops to close in some Baghdad districts on Monday in what they said was the start of a "civil disobedience campaign".
The militia has kept a low profile since Shi‘ite cleric Moqtada al-Sadr called a ceasefire last August and extended it last month, a move U.S. commanders say has helped to sharply reduce violence between majority Shi‘ites and Sunni Muslims. (Additional reporting by Randy Fabi; Editing by Ibon Villelabeitia)