"Today we have decided to go ahead with our planned protests but we have changed strategy and instead of a peaceful march we will seek a confrontation," Samory Ould Beye, a union leader, told the AFP news agency.
Ould Cheikh Abdallahi was overthrown on August 6, hours after he issued a decree firing the military's top brass, including Ould Abdel Aziz, who was the commander of the presidential guard.
Since the coup, the generals have taken over the powers of the president and formed a new government with the support of a majority of the deputies in parliament.
The new leadership has promised to hold elections quickly, but no date has been set and parliament has voted to delay a presidential vote by at least a year.
In a related development, a delegation of generals met African Union officials in Addis Ababa, one day after an AU deadline for reinstating the deposed president passed unheeded despite the threat of sanctions.
Jean Ping, the AU chief, "took the opportunity ... to reiterate the African Union's standpoint" that Mauritania should reinstate Ould Cheikh Abdallahi, the organisation said in a statement after the meeting.
The statement said that "in the face of the absence of a return to constitutional order" in the west African country, its Peace and Security Council would make propositions "at the right time" on how to move forward.
The army says Ould Cheikh Abdallahi has been kept under house arrest but his daughter says his whereabouts are unknown.