The West African country is facing an insurgency by groups linked to al Qaeda and Islamic State.
Large swathes of land have been taken over and millions displaced in the wider Sahel region.
On Saturday (January 21) Burkinabe national television reported that the government had suspended a 2018 military accord with Paris on January 18 - giving France one month to withdraw its troops.
The next day French President Emmanuel Macron said he was awaiting clarifications from transitional president Ibrahim Traore.
But on Monday government spokesman Rimtalba Jean Emmanuel Ouedraogo said "we don't see how to be more clear than this".
The vision of the Burkinabe transitional government, according to Ouedraogo, is for the country to defend itself.
He added that it was not the end of diplomatic relations with France and that Burkina Faso still wanted support in the form of military equipment.
French authorities did not immediately respond to requests for comment.
But French influence in its former colonies has been declining.
That could be seen in the Burkinabe capital Ouagadougou on Friday (January 20).
Hundreds gathered calling on the French army to "get out" and burning French flags.
Both Burkina Faso and neighboring Mali are ruled by military juntas that seized power in the past two years, and have burned bridges with traditional allies.
Last year French troops pulled out of Mali after a deterioration in relations.
That departure coincided with the Malian junta's decision to hire Russian mercenaries to help it fight insurgents.
Macron has accused Russia of "predatory" influence in troubled African countries.
Burkina Faso has not confirmed or denied recent reports that it has also decided to hire Russia's Wagner group.
