Yaya Dillo Djerou, who calls himself leader of a similar group called Platform for Change, National Unity and Democracy (SCUD), said some of his men participated in Sunday's attack.
"A few of our troops have participated in the action in Adre but it is being led by RDL," Djerou told Reuters. "Yesterday we took control of the city," he said. But he declined to say if they were still in control.
The deserters, also accused of attacking army bases in the capital N'Djamena, have demanded President Idriss Deby resign.
Deby hails from the Zaghawa tribe, which spans both sides of the border and is one of the main Darfur rebel tribes.
A number of Darfur rebel commanders fought in the uprising which brought Deby to power, a revolt which was launched from Sudan's remote west, a vast area the size of France.
Doumgor said on Sunday Chadian forces would chase the rebel elements over the frontier into Sudan if necessary.
A Sudan foreign ministry spokesman denied any involvement.
Sudanese army sources reported sporadic fighting in recent days, crossing over the long, porous border between the countries, but said the Sudanese army was not involved.
Both Darfuri rebels and aid workers in the region have reported large troop movements over the past two weeks near the border, with reports of Chadian troops patrolling on the Sudanese side of the border.
(Additional reporting by Dany Danzoumbe Padire in N'Djamena)