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U.S.-led forces in Afghanistan have stepped up security following the shootings out of concern about retaliatory attacks. The U.S. Embassy also has warned American citizens in Afghanistan about the possibility of reprisals. As standard practice, the coalition increased security following the shootings out of concern about retaliatory attacks, said German Brig. Gen. Carsten Jacobson, a coalition spokesman.

Two U.S. defense officials said that an investigation has been started by the Army Criminal Investigation Division but that it was too soon to say when any charges might be filed. They spoke on condition of anonymity because they were not authorized to speak about the issue.

The Afghan Defense Ministry said the gunman left the base in Panjwai district and walked about one mile to Balandi village. Villagers described how they cowered in fear around 3 a.m. as gunshots rang out and 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 after he killed them.

Eleven of the 12 civilians killed in Balandi were from the same family. The remaining victim was a neighbor.

From Balandi, the gunman walked roughly one mile to the village of Alkozai, which was only about 500 meters from the American military base. There, the gunman killed four people in one house and moved on to Mr. Zahir’s house.

U.S. officials said initial reports indicated that the soldier returned to his base after the shootings and turned himself in.

Some Afghan officials and local villagers expressed doubt that a single U.S. soldier could have carried out all the killings 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 two kilometers and enter another house, kill civilians and burn them,” said Abdul Rahim Ayubi, a lawmaker from Kandahar province who visited the area on Monday.

Some villagers also told officials there were multiple soldiers and heard shooting from different directions, but many others said they saw only a single soldier.

NATO insisted there was only one gunman.

“There’s no indication that there was more than one shooter,” Col. Cummings said.

Agha Lalia, a member of the Kandahar Provincial Council who is from Panjwai district, said he talked to two people who were injured in the shooting at a hospital at Kandahar Air Field, where they are being treated by coalition medical personnel. Both said they saw only one soldier shooting.

Associated Press writers Rahim Faiez, Amir Shah, Heidi Vogt and Deb Riechmann in Kabul and Pauline Jelinek in Washington contributed to this report.