After the killing of Afghan civilians by an American soldier Sunday, Republican presidential candidate Newt Gingrich said it was time for U.S. troops to leave Afghanistan.

Though he stopped short of calling for immediate withdrawal, Gingrich said on “Fox News Sunday” that he did not think the mission in Afghanistan was “doable,” the Los Angeles Times reported.

“It’s very likely that we have lost — tragically lost the lives and suffered injuries to a considerable number of young Americans on a mission that we’re going to discover is not doable,” he said, adding in an interview on CBS' “Face the Nation” that the U.S. doesn't have the willpower or the capacity to fundamentally change the region.

But other Republicans, while condemning the murders, said they must not weaken America's resolve in Afghanistan.

The U.S. could “win this thing. We can get it right,” said Sen. Lindsey Graham, R-S.C., on ABC’s “This Week.” “The surge of forces has really put the Taliban on the defensive.”

Sen. John McCain, R-Ariz., said: “I understand the frustration and I understand the anger and the sorrow. I also understand and we should not forget the attacks on the United States of America on 9/11 originated in Afghanistan.

“And if Afghanistan dissolved into a situation where the Taliban were able to take over or a chaotic situation,” McCain added on Fox, “it could easily return to an al-Qaida base for attacks on the United States of America.”

Their comments came shortly after reports that a U.S. Army sergeant went on a house-to-house shooting spree in a village near his military base in southern Afghanistan, killing 16 people, most of them women and children, and wounding several others.

The NATO-led coalition said Sunday that the killer had been detained.

Senate Majority Leader Harry Reid, D-Nev., on CNN’s State of the Union, joined many other officials in expressing sympathy for the victims.

“Our hearts go out to these innocent people,” said Reid. “Our troops are under such tremendous pressure in Afghanistan. It’s a war like no other war we’ve been involved in. But no one can condone or make any suggestion that what he did was right because it was absolutely wrong.”

Asked whether the U.S. should hasten a pullback from Afghanistan, Reid said he believes the U.S. is on the “right track to get out of Afghanistan just as soon as we can.”

These killings only serve to reinforce the mindset that the whole war is broken and that there's little we can do about it beyond trying to cut our losses and leave, Joshua Foust of the American Security Project, told Reuters.