A killing spree by a US soldier in Afghanistan that left 16 civilians dead reignited debate Sunday over the US exit strategy from a decade-old war amid growing resentments and the threat of a violent backlash.

President Barack Obama called Afghan President Hamid Karzai to express his shock and sadness, and promise to hold accountable whoever was responsible.

"This incident is tragic and shocking, and does not represent the exceptional character of our military and the respect that the United States has for the people of Afghanistan," Obama said.

His comments were echoed by the top US commander in Afghanistan, General John Allen, and US Defense Secretary Leon Panetta, who both emphasized the need for continued US-Afghan cooperation.

But the shooting spree, which erupted early Sunday when a US soldier walked out of his base in southern Kandahar province and opened fire on men, women and children in a shocking rampage, raised the threat of another bout of anti-Western violence.

"There's something profoundly wrong with how we're approaching the whole region and I think it's going to get substantially worse, not better," said Republican presidential hopeful Newt Gingrich.

"I think it's very likely that we have lost, tragically lost, the lives and suffered injuries of a considerable number of young Americans on a mission that we're going to discover is not doable," he said on Fox News Sunday.

Obama has set a 2014 deadline for the withdrawal of the 130,000-member US-led NATO force from Afghanistan, even as Washington juggles the training of Afghan security forces to take their place and possible negotiations with the Taliban.

But US relations with its Afghan partners have plunged to an all-time low in the meantime, putting immense strains on a military mission that is now over a decade old and only getting messier with time.

Deadly riots sparked by the accidental burning of Korans by US troops, the murders of US troops allegedly by Afghan counterparts, and a video showing marines urinating on the corpses of slain insurgents are only the latest signs of a deepening estrangement between the NATO force and their Afghan allies.

In Kabul, Karzai condemned Sunday's killings as "unforgivable," opening a new round of recriminations with Washington, where one prominent member of Congress singled out Karzai as "a major question mark" over the US exit strategy.

"The great weakness in Afghanistan is Karzai. Nobody seems to trust him or like him," said Senator Charles Schumer of New York on ABC's "This Week."

The tensions seem certain to complicate Washington's efforts to negotiate a long-term strategic partnership with Kabul that would set the basis for a continuing security relationship after US troops withdraw.

"This tragic incident does not reflect the commitment of the US military to protect the Afghan people and help build a strong and stable Afghanistan," Panetta said.

"As I told President Karzai, I am fully committed to ensuring that our cooperation continues," he said. "It is essential to forging a more peaceful future for the citizens of both our countries."

But a new Washington Post-ABC News poll highlighted another problem: 60 percent of Americans believe the war has not been worth fighting.

Fifty-five percent of those surveyed said they believe Afghans oppose what the United States is doing and 54 percent said the United States should withdraw its forces even if the Afghan army is not adequately trained.

Panetta told reporters last month he hopes the US forces in Afghanistan can make the transition from combat to training and advising the Afghan forces by mid-2013.

"I think that we're on the right track to get out of Afghanistan just as soon as we can," Senator Harry Reid, the top Democrat in the US Senate, said on CNN Sunday.

"I think some of the things that are going on we didn't expect would happen this quickly. There's peace talks starting in Qatar. Taliban have set up offices there. There's conversations going on."

Others argued that it was crucial that US special forces units and air bases remain in Afghanistan after 2014 to ensure the country is not used again as a base for attacks on the United States.

"We should not forget that the attacks on the United States of America originated in Afghanistan," Senator John McCain told CNN.