Nassour said the deserters had escaped into Sudan after government troops laid siege to their hideout in the eastern town of Hadjer Hadid, where they sought refuge earlier this month.
Leaders of the deserters say they number around 600 soldiers and are demanding the resignation of Chad's President Idriss Deby, according to media reports. They call themselves the Platform for Change, National Unity and Democracy (SCUD).
The government said only 40 soldiers had deserted but some had subsequently given themselves up.
"The national army went to hunt down the insurgents ... They then fled into Sudan," Nassour, also minister of territorial administration, told reporters.
"We hope the Sudanese government will disarm them as soon as possible or will let us do so instead."
Nassour said the army had twice launched operations to hunt down the dissident soldiers.
"The army was instructed to neutralise the deserters and encircled them ... Feeling the pressure, the insurgents took off towards the Sudanese border," he said.
Nassour said the soldiers were joined by other individuals in Hadjer Hadid, but added the "situation was under the control of the Chadian army."
Relations between Chad and Sudan have been strained by a 2-1/2 years conflict in Darfur, which has sent hundreds of thousands of refugees streaming into poor, arid eastern Chad.