Emmanuel Macron has promised a minimum wage increase and tax concessions as he addressed the nation for the first time since anti-tax demonstrations around France turned into violent protests.

Speaking in a televised address to the nation, the French leader acknowledged the “anger and indignation” among the public was “deep, and in many ways legitimate”, but vowed “no indulgence” would be given to those behind the violence.

The beleaguered president spoke out after four weeks of protests, which started in neglected provinces to oppose fuel tax increases and progressed to rioting in the capital.

“We are at a historic moment for our country,” Mr Macron said as he responded to the protesters demands by promising a raft of new measures.

“We will respond to the economic and social urgency with strong measures, by cutting taxes more rapidly, by keeping our spending under control, but not with U-turns,” he added.

Under plans announced on Monday evening, the minimum wage will increase by €100 per month and taxes on overtime pay will be abolished from 1 January – several months ahead of schedule.

Mr Macron also said a tax hike pensioners faced would be scrapped as he tried to placate a growing number of protesters who present a increasing challenge to his authority. However, the former banker – who has been dubbed “the president of the rich” by his critics – refused to reinstate a controversial wealth tax on all those with assets of more than £1.1m.

The measures announced by Mr Macron to appease the protests will cost between €8bn to €10bn euros (£7.2bn to £9bn), a junior minister said after the president’s TV address.

“It’s between 8 to 10 billion euros,” Olivier Dussopt, junior minister for public accounts, said on BFM TV. “We are in the process of fine-tuning and to see how to finance it.”

After keeping public comments about the protests to a minimum, Mr Macron admitted that many people were unhappy with living conditions and felt they “had not been listened to”.

He promised that “all means” would be used to restore calm and, in a rare concession, acknowledged some of his remarks may have been ill-judged.

“I may have given the impression that it wasn’t my problem, that it wasn’t my priority. I may have hurt some of you with my words,” he said.

Protesters set fire to overturned cars in central Paris after police pushed them away from the Arc de Triomphe in violent clashes

The French president opened his address by condemning the violence, telling viewers that ”no anger justifies attacking a gendarme, or a police officer”.

But, he conceded, “this anger is shared by many among us, by many French people”.

“Their distress doesn’t date from yesterday. We have ended up getting used to it,” he said.

“These are 40 years of malaise that have come to the surface. Without doubt we haven’t been able to provide a response that was strong or quick enough.”

It remains unclear whether Mr Macron’s remarks will placate the protesters, many of whom had said they would only be happy with the president’s resignation.

Before his TV speech, Mr Macron met with local and national politicians and with union and business leaders to hear their concerns – but with no representatives of the scattered, leaderless protest movement.

Small business representatives lamented the blow the demonstrations were dealing to retail and other companies at the height of the Christmas shopping season.

Finance minister Bruno Le Maire said new measures should focus on helping France’s working classes.

“We are ready to make any gesture” that works, he said on RTL radio. “What is important now is to put an end to the crisis and find peace and unity in the country again.”

Fallout from the protests so far could cost France 0.1 per cent of gross domestic product in the last quarter of the year, Mr Le Maire warned.

Clashes at the Paris fuel protests: in pictures Show all 29 1 /29 Clashes at the Paris fuel protests: in pictures Clashes at the Paris fuel protests: in pictures Water cannons are turned on the protesters Reuters Clashes at the Paris fuel protests: in pictures Riot police detain protesters EPA Clashes at the Paris fuel protests: in pictures A car is set alight in the protests AFP/Getty Clashes at the Paris fuel protests: in pictures The Arc de Triomphe is graffitied with the slogan: 'he yellow vests will triumph' Reuters Clashes at the Paris fuel protests: in pictures Protesters barricade themselves on the Champs Elysees as police line the streets Reuters Clashes at the Paris fuel protests: in pictures A protester fires at police with a slingshot AFP/Getty Clashes at the Paris fuel protests: in pictures A protester holds up a sign that reads 'your Europe ruins us' Reuters Clashes at the Paris fuel protests: in pictures A protester gestures amidst burning cars EPA Clashes at the Paris fuel protests: in pictures Protesters walk amidst tear gas near the Arc de Triomphe Reuters Clashes at the Paris fuel protests: in pictures A protester runs amidst tear gas Reuters Clashes at the Paris fuel protests: in pictures Protesters on the Champs Elysees amidst tear gas AFP/Getty Clashes at the Paris fuel protests: in pictures Protesters in yellow vests gather outside the town hall in Bordeaux EPA Clashes at the Paris fuel protests: in pictures Protesters gather on the Champs Elysees after the police deploy tear gas AFP/Getty Clashes at the Paris fuel protests: in pictures Protesters stand by the Tomb of the Unknown Soldier in Paris AFP/Getty Clashes at the Paris fuel protests: in pictures A protester waves a French flag Reuters Clashes at the Paris fuel protests: in pictures Riot police take formation AFP/Getty Clashes at the Paris fuel protests: in pictures A general view of the Champs Elysees in Paris today as protesters clash with police Reuters Clashes at the Paris fuel protests: in pictures A protester wears a jacket reading 'Macron, thief, lier, crook, go away, the people banish you' AP Clashes at the Paris fuel protests: in pictures Protesters gather on the Champs Elysees AFP/Getty Clashes at the Paris fuel protests: in pictures Protesters hold a French flag by a burning barricade AFP/Getty Clashes at the Paris fuel protests: in pictures Protesters gather by a fire AFP/Getty Clashes at the Paris fuel protests: in pictures Water cannons are turned on the protesters Reuters Clashes at the Paris fuel protests: in pictures A protester wears an adapted yellow vest reading 'Macron's cemetery: here lies your buying power' AFP/Getty Clashes at the Paris fuel protests: in pictures Protesters gather by a burning car AFP/Getty Clashes at the Paris fuel protests: in pictures Riot police advance through tear gas followed closely by their water cannon EPA Clashes at the Paris fuel protests: in pictures Tear gas is deployed to deter the protesters Reuters Clashes at the Paris fuel protests: in pictures A protester waves a French flag amidst tear gas AP Clashes at the Paris fuel protests: in pictures Protesters walk amidst tear gas by the Arc de Triomphe Reuters Clashes at the Paris fuel protests: in pictures A protester holds a sign asking for the reintroduction of ISF (an old French tax on wealth) AFP/Getty

“That means fewer jobs, it means less prosperity for the whole country,” he said.

The yellow vest protests began in November against a rise in fuel taxes – which Mr Macron retreated from last week – but mushroomed into a plethora of sometimes contradictory demands. Lately, they have included Mr Macron’s resignation.

“Macron is there for the rich, not for all the French,” 68-year-old retiree Jean-Pierre Meunuer said at Saturday’s protest in Paris.

With the new demonstrations planned on Saturday, some police officers who spent multiple weekends on crowd and riot patrol are calling for their own tax-exempt overtime pay.

Key Paris tourist sites reopened on Sunday, including the Louvre museum and the Eiffel Tower, while workers cleaned up tons of debris from Saturday’s protests, which left widespread damage in the capital and elsewhere.

French media reported that 136,000 protesters took to the streets nationwide on Saturday.