(CNN) -- The American military suspect in the killing of 16 Afghan men, women and children has been moved from the outpost where he served to detention in a larger U.S. location in Afghanistan, a U.S. military official told CNN Monday. The official declined to name the new location. The suspect worked in force protection at his outpost and is a conventional army soldier serving in support of the Green Berets, the source said.
Meanwhile, the Taliban vowed revenge Monday for the attack on Afghan civilians.
U.S.-led forces in Afghanistan have stepped up security following the shootings Sunday in Kandahar province out of concern about retaliatory attacks. The U.S. Embassy has also warned American citizens in Afghanistan about the possibility of reprisals.
The Taliban claimed responsibility for several attacks last month that the group said were in retaliation for the Americans burning Qurans. Afghan forces also turned their guns on their supposed allies at the time, killing six U.S. troops as violent protests wracked the country.
There were no signs of protests Monday and it was unclear what the response would be to Sunday's deadly spree. It may not be as dramatic as after the Quran burnings since the desecration of the Muslim holy book is viewed as one of the worst sins in Islam. Afghans have also faced numerous instances of civilian casualties from coalition military operations, though rarely the kind of killings seen Sunday.
But the attack will likely spark even greater distrust between Washington and Kabul and fuel questions in both countries about why American troops are still fighting in Afghanistan after 10 years of conflict and the killing of Osama bin Laden.
The Taliban said in a statement on their website that "sick-minded American savages" committed the "blood-soaked and inhumane crime" in Panjwai district, a rural region outside Kandahar that is the cradle of the Taliban and where coalition forces have fought for control for years.
The militant group promised the families of the victims that it would take revenge "for every single martyr with the help of Allah."
There are still many questions about what happened in the villages of Balandi and Alkozai in Panjwai before dawn Sunday and what motivated the killings.
Afghan President Hamid Karzai condemned the attack and said the 16 dead included nine children and three women. Five other villagers were wounded.
"This is an assassination, an intentional killing of innocent civilians and cannot be forgiven," Karzai said Sunday.
U.S. military spokesman Lt. Col. Jimmie Cummings confirmed Monday that the number of dead was "in the teens" but declined to be more specific, saying U.S. forces had not been given access to independently count the bodies.
U.S. and Afghan officials have said the attack began around 3 a.m. in the two villages, which are fairly close to a U.S. base in a region that was the focus of President Barack Obama's military surge in the south starting in 2009.
Villagers described how they cowered in fear as gunshots rang out while the soldier roamed from house to house firing on those inside. They said he entered three homes in all and set fire to some of the bodies. Eleven of the dead were from a single family.
The burning of the bodies may ignite even more outrage because it is seen as the desecration of corpses and therefore against Islam.
U.S. officials said the shooter, identified as an Army staff sergeant, acted alone after leaving his base in southern Afghanistan. Initial reports indicated he returned to the base after the shooting and turned himself in. He was in custody at a NATO base in Afghanistan.
Some Afghan officials and local villagers expressed doubt that a single U.S. soldier could have carried out all the killings in houses more than a mile apart and burned the bodies afterward.
"It is not possible for only one American soldier to come out of his base, kill a number of people far away, burn the bodies, go to another house and kill civilians there, then walk at least 2 kilometers and enter another house, kill civilians and burn them," said Ayubi.
Some villagers also told officials there were multiple soldiers and heard shooting from different directions. But many others said they only saw a single soldier.
Cummings, the U.S. military spokesman, also said, "There's no indication that there was more than one shooter."
The Afghan defense ministry said Monday that its initial reports indicate one soldier carried out the attacks, but they left open the possibility there could have been be more.
"The Afghan defense ministry requests a trial for the perpetrator or perpetrators of this attack," said a statement.
The soldier suspected of carrying out the attack is from Joint Base Lewis-McChord, Wash., and was assigned to support a special operations unit of either Green Berets or Navy SEALs engaged in a village stability operation, said a U.S. official, speaking on condition of anonymity because the investigation is still ongoing.
Special operations troops pair with villagers chosen by village elders to become essentially a sanctioned, armed neighborhood watch.
A spokesman for U.S.-led forces in Afghanistan, German Brig. Gen. Carsten Jacobson, said the coalition has increased security following the shootings, describing it as standard practice.
"Of course we have taken security measures following yesterday's incident," Jacobson said.
In the wake of the Quran burnings, the top U.S. commander in Afghanistan, Gen. John Allen, visited troops at a base that was attacked last month and urged them not to give in to the impulse for revenge.
The tensions between the two countries had appeared to be easing as recently as Friday, when the two governments signed a memorandum of understanding about the transfer of Afghan detainees to Afghan control - a key step toward an eventual strategic partnership to govern U.S. forces in the country.
Now, another wave of anti-American hatred could threaten the entire future of the mission, fueling not only anger among the Afghans whom the coalition is supposed to be defending but also encouraging doubts among U.S. political figures that the long and costly war is worth the sacrifice in lives and treasury.
Obama phoned Karzai on Sunday to express his shock and sadness, and offered condolences to the grieving families and to the people of Afghanistan.
In a statement released by the White House, Obama called the attack "tragic and shocking" and not representative of "the exceptional character of our military and the respect that the United States has for the people of Afghanistan." He vowed "to get the facts as quickly as possible and to hold accountable anyone responsible."