(Reuters) - Forty percent of Americans say the slaughter of 16 Afghan civilians by a U.S. soldier had weakened their support for the war, a poll showed Wednesday.

Sixty-one percent of Americans surveyed in the March 12-13 online poll by Reuters/Ipsos said the remaining U.S. troops should be brought home immediately, down slightly from the 66 percent who expressed that opinion in a similar poll from early March. Seventeen percent disagreed.

The Obama administration is seeking to contain the fallout from the shocking shooting on Sunday, in which a U.S. staff sergeant walked off his base in southern Afghanistan and shot the 16 civilians, mostly women and children, in a nearby village.

Coming on the heels of violent outcry in Afghanistan triggered by U.S. soldiers' burning of copies of the Quran on a NATO military base, the shooting underscores the challenges the United States and its NATO allies face in the country, where after over 10 years of war the Taliban remains a potent enemy.

Despite ongoing violence, Western nations have begun their gradual exit from this long and costly conflict, and most foreign combat troops are due to withdraw by the end of 2014.

In the poll, 20 percent of those surveyed said the shooting did not make them less supportive of U.S. involvement in Afghanistan. Democrats' support was slightly more likely to have been affected by the weekend incident than that of Republicans, the poll found.

The poll included 1,061 Americans interviewed online, had a credibility interval of plus/minus 3.5 percentage points.

The shooting comes at a delicate moment for President Barack Obama, who is seeking to showcase his foreign policy credentials - including the killing of al Qaeda leader Osama bin Laden last spring - ahead of presidential elections in November he hopes will give him a second term.

U.S. officials have been hoping to conclude a bilateral deal to authorize a modest U.S. troop presence in Afghanistan beyond 2014, which would focus on counter-terrorism and assisting an inexperienced Afghan military.

But the prospects for a swift conclusion to those negotiations appear to have dimmed as Afghans voice their anger over the death of the villagers in southern Kandahar province and demand the United States punish the rogue soldier.

U.S. Defense Secretary Leon Panetta is likely to discuss the fate of the soldier, whose name has not been released, when he meets with Afghan President Hamid Karzai during a visit he is making to Afghanistan this week.

(Editing by Jackie Frank)

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