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Laurent Wauquiez, vice president of Sarkozy's The Republicans party, went further, demanding the prime minister Manuel Valls and interior minister Bernard Cazeneuve step down for failing to do what is necessary to protect the country.

Wauquiez said the law must adapt to terrorism and not vice versa, suggesting French laws were too lenient to deal with the crisis.

Far-right leader of the French National Front party Marine Le Pen accused the political class on both sides of the left-right divide of failing to protect France.

Le Pen called for the immediate closure of "Salafi mosques", in addition to tighter border controls, an end to immigration and the expulsion of terror suspects from France.

Civil liberties vs. security

The main issue of contention between the rightwing opposition and the government seems to be how much civil liberties, rights and due process should be sacrificed for the sake of security. The government argues that everything within the law has been done to protect citizens while the right-wing demand seems to be to amend laws that currently still protect the rights of terror suspects.

France has already declared then extended a state of emergency, giving security agencies broader powers to surveil those suspected of extremist tendencies without permission from the courts

France has already declared then extended the controversial state of emergency, giving security agencies broader powers to surveil those suspected of extremist tendencies without permission from the courts. This affects an estimated 14,000 French citizens and their relatives and friends, according to press reports.

The French president on Thursday revealed a project to create a national guard force comprising reservists. However, the project will take months to implement.

A ban on foreign-funded mosques?

On Friday, under pressure from his critics, France's prime minister said he would consider a temporary ban on foreign financing of mosques, urging a "new model" for relations with Islam after a spate of extremist attacks.

Manuel Valls, under fire for perceived security lapses around the attacks, also admitted a "failure" in the fact that one of the extremists who stormed a church and killed a priest 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."

Valls also called for imams to be "trained in France, not elsewhere."

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 extremist 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.

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.

The electronically tagged Kermiche was allowed out of his home on weekday mornings, enabling him and his accomplice to storm a church in the Normandy town of 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.

'Advanced concealment methods'

In the government's first admission of failure since the two attacks, Valls acknowledged Kermiche's liberty was a "failure, it has to be recognised", adding that judges needed to take a "different, case-by-case, approach, given the extremists' very advanced concealment methods".

But he said it was "too easy to hold judges responsible for this act of terrorism."

Meanwhile a source close to the investigation said a Syrian asylum seeker had been taken in for questioning after being arrested at a refugee center in Alliers, central France.

A 30-year-old member of Petitjean's family and a 16-year-old whose brother traveled with Kermiche are also in custody.

In a newly released video, Petitjean pledged to attack France, directly addressing President Francois Hollande and Valls.

The French government has said that everything possible is being done to protect citizens, while warning that more terror attacks are inevitable, after three major strikes and several smaller attacks in the past 18 months.

In a newly released video, Petitjean pledged to attack France, directly addressing President Francois Hollande and Valls.

Wearing a striped T-shirt, Petitjean speaks in French laced with Arabic in the footage released by the Amaq news agency linked to the Islamic State group.

He and Kermiche pledged allegiance to IS in a video made before they murdered Hamel that emerged afterwards.

Hamel's funeral will be held in the Gothic cathedral of nearby Rouen next Tuesday.

On Friday, France will observe a day of fasting and prayer called by the French Catholic Church "for our country and for peace in the world".

The church attack was the third in two weeks in France and Germany in which extremists have pledged allegiance to IS, increasing jitters in Europe over young, often unstable men being lured by the group's propaganda and calls to carry out attacks on home turf.

Agencies contributed to this report.