PARIS (Reuters) - French police staged protests in Paris and other cities for a third night, with political opponents seizing on the unease to accuse Francois Hollande’s government of failing on security just months before a presidential election.

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Police say they are no longer sufficiently equipped even to defend themselves and have staged three nights of unauthorised demonstrations.

Hundreds of officers protested at the Place de la Republique square and the Champs Elysees avenue in Paris. Other protests took place in Bordeaux, Nancy and Toulouse.

Right-wing opponent Alain Juppe, the man polls suggest will become next president, on Tuesday decried what he called a loss of authority in the country, while Nicolas Sarkozy, also in the running for president, did likewise in even harsher terms.

A member of his own party also raised pressure on Hollande by calling on him to get tougher on gangland crime and stand aside to allow someone like Prime Minister Manuel Valls to run for president in the election in April and May next year.

“We need someone else with a strong personality to come forward, someone who can offer hope,” said Malek Boutih, a Socialist member of the lower house of parliament.

“It’s normal that these guys (police) are frightened,” said Boutih, representative of a constituency south of Paris where a commando-style gang petrol-bombed four police officers inside their parked police car two weeks ago.

Two police officers were seriously injured in the assault.

“The thugs in question are not just delinquents, some of these people are people who help terrorists who assassinate French people and police,” Boutih told RTL radio.

Media coverage of law and order problems frequently mounts ahead of elections, although this time security has overtaken economic woes as a focus of voters after Islamist-linked attacks that have killed more than 230 people in the past two years.

Thousands of police and soldiers have been deployed to boost security at airports, stations and schools after the attacks.

Boutih’s comments coincided with publication of an opinion poll in which 59 percent of respondents wanted Valls to run, versus 40 percent for Hollande, who has yet to say if he is seeking re-election.

Interior Minister Bernard Cazeneuve met police unions on Tuesday and urged calm, saying the government was supportive of the police and had recruited two-thirds of some 9,000 police staff after a drop of 12,000 under ex-president Sarkozy.

Sarkozy, president from 2007 to 2012, rounded on Cazeneuve and Hollande, saying violent crime was not about police numbers but insufficiently harsh treatment of criminals by the courts.

“I understand the anger of the police,” said Sarkozy. “I’ve never seen such an erosion of authority in this country,” he told Europe 1 radio.