Prime Minister Edouard Philippe said he would make "concrete proposals" on Saturday to end the deadlock with unions over the pension reform.
French unions called on Friday for the strike against a controversial pension reform to continue after days of negotiations with the government failed to produce any breakthrough.
Talks between the government and unions resumed on January 7 after a holiday break during which the ongoing social movement crippled the transport system, leaving thousands stranded for Christmas.
But as the week ended, and despite President Emmanuel Macron calling for "rapid compromises" in his New Year's address, no agreement was found.
Francois Hommeril, president of the CFE-CGC union told reporters after his meeting with Prime Minister Edouard Philippe that the strike is "bound to continue" and that a "series of mobilisations" planned for Saturday and next week will go ahead.
"We are still opposed to this reform as it is presented to us. It is a useless reform, a dangerous reform," he went on, calling for the government to scrap it altogether.
Another union leader, Laurent Berger from the CFDT, struck a slightly more positive note after his own meeting with Philippe, telling reporters that he had felt "a willingness" from officials to discuss quickly adding however that he remains fundamentally opposed to the government's proposed "pivot age".
"The ball is in the government's camp," he then said in a statement, explaining that his union had called for a conference to discuss the best ways to finance a pension reform.
"This proposal only makes sense if the government withdraws its bill on the pivot age," he added.
The Prime Minister described the latest round of talks as "very constructive" said that "good progress in the search for a compromise" had been made. He added that he would present "concrete proposals" on Saturday.
The government wants to overhaul the pension system by rolling the 42 different plans into a universal one.
The plans would also see pension payouts calculated from salaries from across the whole career instead of just the last five years of activity, which unions say would result in much smaller payouts.
The government also wants to phase out the early retirement advantages certain sectors — primarily in the civil service — enjoy by adjusting the so-called "hardship" criterion.
But the introduction of a "pivot age" has been the most controversial issue with unions accusing the government of trying to surreptitiously increase the legal retirement age. Under the government's current plan, workers would only receive their full pension is if they work to a "pivot age" of 64.
They would, however, receive less if they stop working at 62, the country's current legal retirement age, and more if they continue working past 64.
The strike had reached its 37th consecutive day on Friday, making it the longest protest in more than 50 years.
A general strike on Thursday mobilised hundreds of thousands — 1.7 million according to organisers but just 450,000 according to the government — across the country with rallies held in most major cities.
Unions have called for similar rallies to be held on Saturday and Tuesday.
Rail travel will continue to be disrupted over the weekend, the state-owned SNCF railway company warned, but traffic should be "significantly improved".
The company estimates that four out of every high-speed trains will run as scheduled on Saturday and Sunday. Cross-country services will be more impacted with just two out of every five train running but international services, including Eurostar, should only be "slightly disrupted".