Chad's foreign minister said the troops then chased the rebels into Sudan and destroyed their bases across the border.
Scores of Chadian soldiers deserted their barracks in late September before regrouping near the border to stage attacks against the government. The government has accused Sudan of helping the deserters and using them to fight rebels in Darfur.
The deserters launched a failed offensive on the town of Adre on Sunday but were pushed back in fighting that claimed over 300 lives. This ups the official death toll from around 100 although the claim could not be independently verified.
"In its flight the enemy abandoned about 300 bodies and more than 100 injured," the army said in a statement on Monday, adding that five soldiers and three civilians were also killed.
Ahmat Allam-Mi, Chad's foreign minister, said in a statement: "These attacks were repulsed by the national army, which using its right of pursuit, destroyed some of the rebellion's bases in Sudanese territory."
The clashes raised tensions in Sudan's Darfur where rebels have fought Sudan's central government for almost three years.
Hourmadji Moussa Doumgor, Chad's communication minister, said military operations in Adre were continuing on Monday.
"The clean-up is continuing," he said.
"In its flight the enemy abandoned about 300 bodies and more than 100 injured"
Statement by Chad army
Doumgor said army deserters allied to the rebel Rally for Democracy and Liberty (RDL) mounted Sunday's attack.
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 said. "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.