French authorities have imposed overnight curfews in parts of central Paris and other cities after a weekend of riots and looting across the country.

Police in Paris said a curfew would be in force between 23:00 local time (21:00 GMT) and 06:00 in Place de la République, where protesters had gathered over the weekend, and the Les Halles shopping area.

A ban on unauthorised gatherings has also been imposed in several other parts of the city centre.

Partial curfews variously restricting the movement of young people and gatherings were announced for cities including Marseille, Bordeaux, Nice and Lyon in the south as well as Lille and other towns in the north.

Earlier Interior Minister Laurent Nuñez, who has been strongly criticised by opposition politicians over the preparedness for the disorder but whose resignation was rejected by President Emmanuel Macron, admitted police had "lost control" in some cities.

The protests began last month with students demanding better school conditions, but they have have since escalated to take in a broader range of concerns, with numbers at demonstrations this weekend bolstered by trade unions and various protest groups.

More than 2,500 people have been arrested, officials said. One demonstrator's hand was blown off by a police crowd-control grenade, according to the AFP news agency. About 1,000 police officers were injured.

Following a crisis meeting on Monday, the prime minister said local mayors were being given the power to implement curfews "where they need", without specifying which cities where they would be enforced.

Prime Minister Sébastien Lecornu, who did not rule out imposing a state of emergency in the country, said the government would also set aside money to help affected areas recover from the damage, and the funding would be recovered from those behind the violence.

"There will be a law that will be put in place to find ways of making sure that those who have damaged properties will have to pay," Lecornu said.

He also announced a partial unemployment fund for those who could not work as a result of the riots and looting.