Hassan Khamis, a commander in the Darfur rebel National Movement for Reform and Development (NMRD), said: "The Janjawid attacked this morning and killed 12 innocent civilians, including one man who was over 60 years old."
A source in the government in Darfur confirmed the attack on Monday.
"It was Arab nomads," he said, asking not to be identified. "We are not sure yet of the details, but the governor has gone to the site of the attack."
The attack was on the Abu Surooj village northwest of the main town, el-Geneina.
Fighting in Chad
The NMRD controls areas along the border with Chad, which has seen sporadic fighting in recent days between Chadian government forces and deserters.
On Sunday, Chad's communications minister said government troops had repulsed a rebel attack on a town near the border and blamed Sudan for the fighting that killed 100 people.
Sudan said it was not involved.
The violence involving troops from Chad comes amid a surge in fighting involving Sudanese rebels and militias.
The United Nations this month grounded some aid flights and evacuated workers in parts of West Darfur State because of the escalating violence.
Tens of thousands have been killed in Darfur since February 2003, when rebels, saying they had been marginalised by the government in Khartoum, took up arms. More than 2 million people have been driven from their homes.
Peace talks are under way in the Nigerian capital, Abuja, to reach a deal to end the conflict.