Riot police and protesters have fought running battles in the centre of Paris as gilets jaunes anti-government demonstrators in fluorescent yellow vests led street marches over what they called “a crisis” of high taxes and economic inequality.

Less than a week after the fire that destroyed the roof and spire of Notre Dame Cathedral, firefighters rushed to put out multiple small fires around the Place de la République, as motorbikes, bins, bicycles and cars were set alight on roads and pavements. Groups of masked men threw projectiles and police fired teargas. Some rioters in masks smashed the window of a sports shop and ran in to loot it, emerging with bags full of goods.

The interior minister, Christophe Castaner, said on Saturday that Paris could become “the capital of rioting”, suggesting extremist demonstrators planned to attend the street marches. Politicians from Emmanuel Macron’s La République En Marche party said “black bloc” masked anarchist protesters were present.

The street demonstrations had begun peacefully in Paris on Saturday morning – the latest in five months of gilets jaunes demonstrations that began as a fuel-tax revolt in November and have morphed into an anti-protest movement in response to the government’s tax and social policies.

Marching from outside the economy ministry, protesters calmly carried French flags with slogans against Macron written on their yellow vests, such as: “Macron, you take from the poor to give to the rich.”

Some carried banners slamming the “hypocrisy” of wealthy billionaires pledging a total of more than €1bn (£865m) to rebuild Notre Dame Cathedral, saying business leaders had done nothing to address low salaries and the plight of people who couldn’t make ends meet. “Humans first, €1bn for the gilets jaunes,” read one banner.

“Millions for Notre Dame, what about for us, the poor?” read a sign worn by a demonstrator. “Everything for Notre Dame, nothing for Les Misérables,” read another sign that evoked Victor Hugo’s novel.

Riot police fire teargas at protesters. Photograph: Julien de Rosa/EPA

Many protesters said they were frustrated that the international effort to help the fire-damaged cathedral had eclipsed their yellow vest movement against wealth inequality.

In the early afternoon, police clashed with protesters near Place de la République in central Paris. The area was saturated with teargas and men, many with their faces wrapped in bandanas, began pulling individual motorbikes into roads and torching them, the air thick with smoke. Some bins and bicycles were also torched.

Five days after 500 Paris firefighters had battled for nine hours to contain the Notre Dame blaze, fire officers worked to put out the multiple small street fires.

By mid-afternoon, the Paris police issued an appeal on social media for peaceful yellow vest demonstrators to leave Place de la République in order to clearly distance themselves from masked rioters. Police fired teargas and stun grenades and a water cannon was used.

One banner on a statue in Place de la République read “Vive Assange”, expressing support for Julian Assange after his arrest by British police earlier this month.

By 5pm, as hundreds remained in the area, the main square was largely calm, with occasional clashes between police and demonstrators on side streets. Police began moves to clear the remaining crowds.

Meanwhile, a second, authorised peaceful yellow vest protest marched from the northern edge of Paris down to the centre.

Paris police said authorities detained more than 200 people on Saturday and had carried out spot checks of more than 17,000 people who had tried to enter the capital for the protests before the demonstrations or attempted to join them.

The interior ministry said the numbers of demonstrators was up on the previous Saturday, estimating that more than 27,900 people had marched across France, with 9,000 in Paris.

When Notre Dame cathedral caught fire on Monday night, the centrist French president Macron cancelled a speech in which he was to make policy announcements aimed at calming the yellow vest movement. He will instead give a long press conference on Thursday – the first since he was elected two years ago.

“We’re waiting for strong measures from the government that we still haven’t seen, and there’s an urgency to act on democracy, tax, society and the environment,” said one yellow vest protester in Paris.