File Photo: Algerian president Abdelmadjid Tebboune. AFP
The diplomatic spat has been fuelled by a visa row and media reports that President Emmanuel Macron told descendants of fighters in Algeria's 1954-1962 war of independence that the North African country was ruled by a "political-military system" that had "totally re-written" its history.
"Macron completely pointlessly revived an old conflict," Tebboune told German magazine Der Spiegel.
"I won't be the one to make the first move" to ease tensions, he added.
"No Algerian will accept it if I get in touch with those who insulted us."
French daily Le Monde in early October quoted Macron as saying: "Was there an Algerian nation before French colonisation? That's the question."
The comments reflected "the old hatred of colonial masters, and I know that Macron is far from thinking like this," Tebboune said.
Algeria has recalled its ambassador from Paris and banned French military planes from its airspace over the tensions.
Asked by Der Spiegel if the fallout was likely to be resolved any time soon, Tebboune was defiant.
"No, if the French want to go to Mali or Niger now, they will just have to fly for nine hours instead of four," the Algerian president said, referring to two countries where France has sent troops to help fight jihadists.
He said he would however make an exception to "rescue wounded people".
At the end of September, France said it would sharply reduce the number of visas it grants to citizens of Algeria, Morocco and Tunisia, accusing the former French colonies of not doing enough to allow illegal immigrants to return.