"We have clearly expressed our ideas, our concerns and our priorities. We listened to each other. It's true, we do not always agree, but we can still talk together to find compromises," Prime Minister Edouard Philippe said in statement.
"It is therefore important that social dialogue continues in January," he added after he met with trade unions on Monday.
With the aim, Philippe pledged to restart talks with unions on pension reform on Jan. 7. Separate talks will also be held with teachers' and hospital workers' unions from Jan. 13.
Laurent Pietraszewski, minister of state for pensions, said the government is ready to compromise.
"The government is making proposals. When we guarantee acquired rights, when we clearly say that whatever the pension system is, all those within 17 years of retirement would not be affected, we should be able to calm down," he told BFMTV news channel on Tuesday.
However, Philippe Martinez, leader of General Confederation of Labor CGT union, said, "For the moment, nothing has changed," adding, "The disenchantment is here and the strikes are continuing."
The government wants to end all special schemes in current system that allow workers in certain public sectors to retire earlier than average and with more benefits. Under the new system, all pensions will be calculated in a point-based way, with same rules applying to all. The legal retirement age remains 62 but people must work till 64 to qualify for a full pension.
Supporters say the overhaul aims to restore social justice and plug a pension deficit due to stand between 7.9 billion euros (8.75 billion U.S. dollars) and 17.2 billion euros by 2025 if nothing was done. Critics fear citizens will have to work longer while ultimately earning lower pensions.
"This reform has primarily a budget target. The government wants to reduce spending on social protection while we are saying that a modern country must increase its spending on people's well-being, their health and their retirement. These are two opposite social projects," Martineze told France info radio.
Rejecting a truce before Christmas, transport workers on Tuesday staged the 20th day of strike, reducing trains and metro frequencies and stranded millions of French people who used to travel to spend the holiday with their families.
SNCF rail operator said 40 percent of high-speed trains TGV and 20 of intercity trains run. In Paris, six of 16 metro lines are shut with others provided reduced service.
The SNCF announced it had lost 400 million euros in potential earnings so far. Industry associations suffer up to 60 percent of turnover from the same period in 2018, according to local media.
On Monday, CGT chemical branch decided to halt production at Total's Grandpuits oil refinery and petrol depot southeast of Paris. The oil facility, which supplies the capital and the surrounding region, was already producing at minimum capacity.
It's the second refinery to stop work since unions started nationwide strike against pension reform in early December. Other refineries would join the strike in coming days, which may force the government to tap oil strategic reserves to avoid fuel shortage.
In a show of force, the country's trade union called to step up strike during Christmas holidays and stage fresh mass demonstrations early January.(1 euro = 1.108 U.S. dollars)