Police in Paris have fired tear gas on protesters as a fourth weekend of anti-government protests turned violent.

The clashes came after up to 8,000 demonstrators gathered in the city centre. More than 500 people have been taken into custody.

At least 30 people have been injured in the capital, including three police officers.

The “yellow vest” movement opposed fuel tax rises but ministers say it has been hijacked by “ultra-violent” protesters.

Some 8,000 police and 12 armoured vehicles have been deployed in Paris, and nearly 90,000 countrywide.

Last week, hundreds of people were arrested and scores injured in violence in Paris – some of the worst street clashes in the French capital for decades.

What is happening this weekend?

There have been a number of confrontations. Bins were set alight on the Champs-Elysées and cars were torched on Boulevard de Courcelles, about 2km (1.2 miles) north.

Water cannon were deployed on a street east of the city centre.

TV pictures have shown what appear to be far-right groups setting up barricades. Armoured vehicles are being sent to deal with them, and French media say this is the first time they have been deployed in metropolitan Paris.

Different police tactics

By Hugh Schofield, BBC News, Paris

At the top end of the Champs-Elysées, near the Arc de Triomphe, there are sporadic upsurges of tension when riot police move out from their positions to retake ground and push back the more aggressive of the protesters.

Occasionally projectiles are thrown at the police, and some tear gas – but so far the disorder is contained, and nothing like on the scale of last Saturday.

The police are using different tactics – they’re much more mobile and are using snatch squads to seize identified troublemakers.

Many of those arrested will have been of people journeying to, rather than at, the scene of the protests – and found to be carrying projectiles.

As the day moves on, the government must be hoping that this comparatively restrained level of trouble remains the norm.

Prime Minister Edouard Philippe said the numbers of arrests were greater than during the whole of the previous weekend.

“We will ensure that the rest of Saturday unfolds in the best possible conditions,” he said.

Meanwhile on the outskirts of Paris, protesters blocked Porte Maillot, one of the main routes into the city from the outer ring road. Yellow vests briefly stopped traffic on the ring road itself, the Boulevard Périphérique, before being cleared by police.

Correspondents say more flashpoints are possible on the edge of the city, where it is harder for police to filter protesters.

Demonstrations are being held in several other cities including Lyon, Marseille and Grenoble, where a local leader of the yellow vests is reported to have been arrested.

They have even spread to Belgium. About 70 people were arrested in the capital Brussels but there was no violence.

Protests against climate change are also being held in some French cities, including Paris.

The number of security officers deployed across the country has increased to 89,000, up from 65,000 last weekend.

The security forces are seeking to prevent a repeat of last weekend in the capital, where the Arc de Triomphe was vandalised, police were attacked and cars overturned and burned.

On social media, some activists have called for attacks on police and the Elysée palace in an “Act IV” drama.

One MP, Benoît Potterie, received a bullet in the post, accompanied by the words: “Next time it will be between your eyes.”

Six matches in the top tier of France’s football league have been postponed. The Louvre, Musée d’Orsay and other sites are closed in Paris.

Where are we with the yellow vest movement?

The “gilets jaunes” protesters are so-called because they have taken to the streets wearing the high-visibility yellow clothing that is required to be carried in every vehicle by French law.

The BBC’s Lucy Williamson in Paris says that over the past few weeks, the social media movement has morphed from a protest over fuel prices to a leaderless spectrum of interest groups and differing demands.

Its core aim, to highlight the economic frustration and political distrust of poorer working families, still has widespread support, our correspondent says.

An opinion poll on Friday showed a dip in support, but it still stood at 66%.

President Emmanuel Macron’s ratings have fallen amid the crisis, and he is planning a national address next week, his office has said. Some have criticised him for keeping too low a profile.

What has the government conceded?

The government has said it is scrapping the unpopular fuel tax increases in its budget and has frozen electricity and gas prices for 2019.

The problem is that protests have erupted over other issues.

Granting concessions in some areas may not placate all the protesters, some of whom are calling for higher wages, lower taxes, better pensions, easier university requirements and even the resignation of the president.

Some of Mr Macron’s critics call him “the president of the rich”.