Several ministers in Saleh Abbas's government have been accused of embezzlement in a scandal related to the purchase of school textbooks.
Four ministers have been suspended in recent months on allegations of embezzlement of about $5m of public funds.
Saleh Abbas's popularity has also suffered from the rising cost of living in Chad, one of the poorest countries in the world.
No cabinet meetings have been held since December and political differences have become apparent between President Deby and Saleh Abbas, a former opposition figure who took office in 2008.
Nadingar is the leader of a party which strongly supports Deby.
The prime minister runs the day-to-day running of government in Chad but the president retains a tight grip on decision-making in the West African nation.
Chad is due to hold legislative elections by the end of the year.