Governor Abd al-Rahman told reporters on Monday that the incident occurred on Sunday night in Char Chino district, 330 kilometres south of the capital Kabul, after US soldiers had come to the village of Saranaw in search of suspected fighters.
"A number of villagers were scared that probably they would be arrested by the Americans so they left the village with their families," Abd al-Rahman said.
"As soon as they arrived near a river, planes bombed them and killed 11 innocent civilians."
The dead were four children, three women and four men, he said.
"Today in the morning we went to the site and buried the bodies.
But a US military spokesman said on Monday only five "armed anti-coalition militia members" had been killed on the weekend in Uruzgan province when coalition forces "engaged from the air."
The spokesman had no further details on the incident.
"I personally went and talked to the Americans about why this incident happened. They said that it was a mistake by our planes and that the people near the river had weapon," said Abd al-Rahman.
In air raids conducted by the United States in mid-December about 15 children were killed in Paktia and neighbouring Ghazni province, both in the southeast of the country. Ghazni also neighbours Uruzgan province.
Nine children were also killed in a daylight air attack against suspected Taliban in Ghazni on 6 December.
Six children and two adults had been killed the previous night when a wall collapsed during a combined air and ground assault on a suspected enemy compound in Paktia. The US military said the compound was packed with weapons and explosives.
At the time, the United Nations expressed fears that such attacks by the United States only hindered efforts at peace and stability in the war-ravaged country.
Taliban fighters have strong support in southern and eastern Afghanistan among people who are hostile to the US military and US-backed government of President Hamid Karzai.