Manuel Valls, under fire for perceived security lapses around the attacks, also admitted a "failure" in the fact that one of the jihadists who stormed a church and killed a priest on Tuesday had been released with an electronic tag pending trial.
In an interview with French daily Le Monde, Valls said he was "open to the idea that -- for a period yet to be determined -- there should be no financing from abroad for the construction of mosques."
He said Interior Minister Bernard Cazeneuve, whose portfolio also includes religious affairs, was working on building a "new model" for France's relations with Islam.
Both Valls and Cazeneuve have faced calls to resign after the second jihadist attack in less than a fortnight raised questions over France's vigilance and preparedness.
The government has faced tough questions since it emerged that both church attackers had been on the radar of intelligence services and had tried to go to Syria.
Sparking particular ire was the revelation that one of the assailants, 19-year-old Adel Kermiche, had been released from prison while awaiting trial on terror charges after his second attempt to travel to Syria.
Saint-Etienne-du-Rouvray and slit the throat of 86-year-old priest Jacques Hamel at the altar.
Kermiche's accomplice Abdel Malik Petitjean, also 19, had been on the security watchlist since trying to reach Syria from Turkey.
The church attack came as the government was already facing a firestorm of criticism over alleged security failings after the Bastille Day truck massacre in Nice that left 84 people dead two weeks ago.
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