Prime Minister Sebastien Lecornu ruled out a blanket curfew in Paris but not a state of emergency.
But he said it was more appropriate for now to apply partial and localised curfews, without providing details.
"My determination to restore order is absolute," he told reporters.
Ariel Weil, the Socialist mayor of central Paris, said on BFM TV he favoured a curfew.
Marseille banned gatherings and demonstrations.
French unions meanwhile called for a new round of strikes and rallies on November 5.
The weekend of looting and violence between some protesters and police followed weeks of student demonstrations, rocking France six months ahead of its next presidential election and highlighting pressures from a weak economy and surging debt.
Lecornu blamed "far-left" groups for some of France's worst unrest in years.
"There is, after all, a far-left movement that wants to cause - we can't put it any more strongly - profound unrest in the country in the run-up to the presidential election," he said.
La France Insoumise presidential candidate Jean-Luc Melenchon urged him to provide evidence.
"Otherwise, he should apologise, keep quiet and stop fanning the flames of unrest," he said on X.
The Federation of Trade and Retail said almost 3000 shops had been affected over the weekend.
"Once again, the retail sector finds itself on the front line, at a time when it is already weakened by a succession of crises," it said.
"Behind every ransacked shop are business owners, employees and families who have seen years of work and effort wiped out in a matter of hours," it added, calling for social security and tax relief for affected businesses.
Lecornu said the government would provide furlough measures from Tuesday.
Standing before a boarded-up shopfront, Gerard Nouchi, manager of two clothing stores in Marseille, said there weren't enough police to stop the looters.
"They trashed everything, broke things, insulted us," Nouchi said.
"It was like a real tornado."
The government ordered platforms selling looted goods to take down announcements and collaborate to prosecute resellers, Junior Digital Minister Anne Le Hénanff wrote on X.
About 2400 people were arrested and one protester died from a cardiac arrest on Saturday while nearly 1000 officers were injured, according to the interior ministry.
French assets were underperforming broader European markets on Monday although moves were more contained than at some other moments of recent political friction.
Tensions in President Emmanuel Macron's fragile government over apparent security shortcomings - coming as the government needs to pass a budget bill to rein in its finances - could further unsettle investors.
Macron's office said on Monday he had turned down his Interior Minister Laurent Nunez's offer to resign, telling him instead to put an end to barricades and looting and be transparent over what Macron called "intelligence and foresight failings".
Nunez told reporters that Tuesday evening's Champions League football match between Paris Saint-Germain and Barcelona would go ahead as planned.
The mayors of Paris, Marseille and Lyon said in a joint op-ed in the newspaper Liberation that they were used to demonstrations and protests.
"But on Saturday ... for the first time, we had the feeling that whole sections of our cities had been left without protection," said the mayors, all from centre-left parties.
The start of school holidays on Monday may provide relief but students were staging more gatherings and blockades in some places, including the Louvre gallery and Sciences Po university in central Paris.
