The French government will suspend a fuel tax rise which has led to weeks of violent protests, local media report.
The protests have hit major French cities causing considerable damage for the past three weekends.
Prime Minister Edouard Philippe sought compromise with the protesters, but they called off talks citing death threats from extremists in their ranks.
The “gilets jaunes” (yellow vests) protests have now grown to reflect more widespread anger at the government.
Three people have died since the unrest began and the resulting violence and vandalism – notably when statues were smashed at the Arc de Triomphe last Saturday – have been widely condemned.
“Yellow vests” 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 movement has grown via social media and has supporters across the political spectrum.
President Emmanuel Macron was elected two years ago with an overwhelming mandate for sweeping reform, but his popularity has fallen sharply in recent months.
Mr Macron has accused his political opponents of hijacking the movement in order to block the reforms.
Macron’s difficulty
The protesters have been waiting for the president to enact the next step in the elaborate pas-de-deux which is French social negotiation.
What the ritual requires now is a gesture from the government that shows that it has not just listened, but that it is prepared to appease.
That is how, since time immemorial, French social conflicts have been resolved.
The difficulty for Emmanuel Macron is that this is exactly the kind of capitulation to the street that he has vowed to stop. There will be no change of direction, he repeats to all who will hear, because that would only store up worse problems for the future.
What has the government been doing?
Mr Macron held an urgent security meeting on Monday. Ministers said that while no options had been ruled out, imposing a state of emergency had not been discussed during the talks.
He has also cancelled a planned trip to Serbia to concentrate on the crisis.
Mr Philippe, meanwhile, spoke to leaders of the opposition on Monday. He is due to meet MPs from the ruling party, La Republique en Marche, later on Tuesday.
Finance Minister Bruno Le Maire met business representatives to assess the damage caused to businesses over the weekend.
Some retailers had seen sales drop by around 20-40% during the demonstrations, while some restaurants had lost 20-50% of their takings, he added.
Who are the protesters?
The “gilets jaunes” movement began as a protest against a rise in duties on diesel – which is widely used by French motorists and has long been less heavily taxed than other types of fuel.
Mr Macron says his motivation for the increase is environmental, but protesters call him out of touch – particularly with non-city dwellers who rely on their cars.
The movement later grew to reflect a range of grievances, including the marginalisation of rural areas, high living costs, and general anger at President Macron’s economic policies.
The protests have no identifiable leadership and gained momentum via social media, encompassing a whole range of participants from the anarchist far left to the nationalist far right, and plenty of moderates in-between.
Nearly 300,000 people took part in the first countrywide demonstration. There were more than 106,000 a week later, and 136,000 people last Saturday.
Do the protests show any sign of stopping?
Protests continued into Monday. About 50 “yellow vests” blocked access to a major fuel depot in the port of Fos-sur-Mer, near Marseille, and petrol stations across the country have run out of fuel.
Students in about 100 secondary schools across the country held demonstrations against educational and exam reforms.
Changes affecting ambulance drivers are also part of a raft of reforms by President Macron.
Private ambulance drivers staged further demonstrations on Monday against a range of social security and healthcare reforms they say could affect their services.
One protester told the Reuters news agency: “[The reforms] will bludgeon us financially and destroy our companies. We’re going to have to fire people, that’s for sure.”
It is unclear whether the groups of students and health workers have directly aligned themselves with the “yellow vests”.
One member of the movement, a man in his 20s, is in a critical condition in hospital in Toulouse.
He was injured in a clash with police.
By Hugh Schofield, BBC News, Paris