The new military regime, which overthrew Niger's democratically elected president exactly two months ago, said in a statement released overnight that the timeframe for the pull-out "must be set out in a negotiated framework and by mutual agreement."
French President Emmanuel Macron on Sunday announced that France would withdraw its ambassador from Niger, followed by the French military contingent in the coming months.
He said that military cooperation was "over" and French troops would withdraw in "the months and weeks to come" with a full pull-out "by the end of the year."
France has about 1,500 soldiers in its former colony as part of an anti-jihadist deployment in the Sahel region.
Niger's rulers, who have welcomed the announcement by France, said they were waiting for it to be followed up by official action by French authorities.
France has not recognized the authority of the military leaders and is still demanding the restoration of President Mohamed Bazoum.