Protesters from France’s “gilet jaunes” (yellow vests) movement have pulled out of a meeting with Prime Minister Edouard Philippe scheduled for Tuesday.
Some members of the group said they received death threats from hard-line protesters warning against entering into negotiations with the government.
The “yellow vests” have been protesting about a controversial fuel tax since mid-November.
But the protests now reflect widespread anger at the government.
France’s interior ministry says about 136,000 people took part in the protests nationwide on Sunday.
Three people have died since the unrest began and the resulting violence and vandalism of public spaces 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 to encompass broader criticism of President Emmanuel Macron’s economic policies, with supporters across the political spectrum.
Mr Macron has accused his political opponents of hijacking the movement in order to block his reform programme.
The French president 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.
Mr Macron has also cancelled a planned trip to Serbia to concentrate on the crisis.
Culture Minister Franck Riester told reporters that the Prime Minister Philippe would announce “a strong conciliatory gesture in the coming days”, without giving details.
Mr Philippe also spoke with leaders of the opposition on Monday.
Far-right leader Marine Le Pen, who was at the meeting, warned that Mr Macron could become the first president to give the order to open fire on his own people in 50 years.
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.
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.
Also on Monday, French private ambulance drivers staged further demonstrations 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.