France's government faced criticism of its security record, in the wake of revelations that one of the assailants who slit the throat of a priest at a church altar was a known would-be jihadist under police surveillance.

President Francois Hollande's predecessor and potential opponent in a presidential election next year, Nicolas Sarkozy, said the government must take stronger steps to track known Islamist sympathisers.

Tuesday's attackers interrupted a church service, forced 85-year-old Roman Catholic priest Father Jacques Hamel to his knees at the altar and slit his throat. As they came out of the church shouting "Allahu akbar" ("God is Greatest"), they were shot and killed by police.

The attack in the Saint-Etienne-du-Rouvray church came less that two weeks after another suspected Islamist drove a truck into a Bastille Day crowd, killing 84 people. Opposition politicians have responded to the attacks with strong criticism of the Socialist government's security record, unlike last year, when they made a show of unity after gunmen and bombers killed 130 people in Paris in November and attacked a satirical newspaper in January.

Francois Heisbourg, special advisor for Paris-based think tank Fondation Pour La Recherge Strategique and former security advisor for the defence ministry, said the church attack in Normandy could have been prevented, because one of the perpetrators, Adel Kermiche, was known to be working in a terrorist enterprise and was under house arrest with an electronic tag.

"Obviously, when you have an attack, you failed to prevent. That goes without saying. Whether these attacks could have been prevented, is altogether another question. The one in Nice was probably the most difficult of all to prevent, since the perpetrator was essentially unknown to any police service dealing with counterterrorism, both in France and in his home country of Tunisia, so that's one which would have been a very difficult call," Heisbourg said.

A parliamentary commission recently published a report following a five-month inquiry into the government's security framework. The inquiry was launched after the Charlie Hebdo killings in January 2015.

Heisbourg said the commission made 39 recommendations such as establishing a counter-terrorism center that answers to the chief executive, similar to such entities in the U.S. or the UK. Leaving counter-terrorism solely under the interior ministry is not satisfactory, he said.

Rebuilding community surveillance was another recommendation by the parliamentary commission's report, which was largely ignored by the Hollande government.

On the day of the Nice attacks, Sarkozy said recommendations made by his party, Les Republicains, should be heeded immediately.

"I'm a bit tired of these daily polemics, constantly reiterated, brought on by a certain number of opposition leaders. I think all our energy, and this is the state of mind the president and prime minister would like us to work in, must be completely focused on the fight against terrorism," Interior Minister Bernard Cazeneuve said a day later.

Sarkozy has called for the detention or electronic tagging of all suspected Islamist militants, even if they have committed no offence. France's internal security service has confidential "S files" on some 10,500 suspected or aspiring jihadists.

Cazeneuve rejected Sarkozy's proposal, saying that to jail them would be unconstitutional and counterproductive.

"The government has locked itself into a repetition of what it has already done, that is - more state of emergency, more soldiers, more bombing against Raqqa or Mosul. These three things did not work in the past, it is unlikely that they're going to work much better in the future," Heisbourg said, and called the opposition's calls "grandstanding".

"The sort of donkey work, the in-depth changes and reforms which are required, which are put forward by the parliamentary committee, are for the time being, not being heard, either by the government or by the opposition," he added.

Heisbourg said state of emergency measures, which include extension of exceptional search-and-arrest powers for police, are not necessarily effective, instead counseling better surveillance.

"The only way to try to preempt the sorts of things which happen in France or in Germany very recently, or in Belgium, will require much more surveillance of society in general, and not simply of would be perpetrators," he said.

Since the Bastille Day killings in Nice, there has been a spate of attacks in Germany as well, creating greater alarm in Western Europe already reeling from attacks last year in France and this year in Brussels.