The French government has begun crucial talks with unions to try to end the stand-off over pensions reform that has sparked the country’s longest transport strikes in decades.

The prime minister, Édouard Philippe, hinted that both sides could compromise, saying he was “open to any discussions of the terms” of the changes and the thorny issue of retirement age.

The protest against Emmanuel Macron’s flagship pensions reform has lasted longer than any strike since the wildcat workers’ stoppages of May 1968. The rail stoppage, which began on 5 December, is now France’s longest continuous train strike since the national service was created in the 1930s.

The president has insisted the crisis be calmed, but his political identity rests on his resolve to push through changes while not appearing to concede too much to the strikers.

The government insists it will create a single, universal points-based pensions system for all, getting rid of dozens of different special systems for sectors ranging from rail and energy workers to lawyers and Paris opera staff. But there is a major sticking point over the government’s additional aim to tinker with France’s retirement age.

Philippe has argued that, to balance the pension budget, workers would be incentivised to stay in the labour force until 64 in order to take home a full pension, instead of leaving at the official retirement age of 62. Unions fear people will be made to work longer for lower pensions. Even moderate unions are angry at any effective change to the retirement age.

The key is whether the government can this week agree a compromise on this point with more moderate unions in order to calm the strikes. Grassroots transport workers are holding a harder line than leaders. One rail worker in a Paris suburb said he had lost so much salary during the strike that he would not give up now unless the government made major changes to its plans.

The rail strikes, which have led to more than €600m in lost ticket sales for the national rail operator, SNCF, are continuing to cause major disruption, particularly for commuters in the greater Paris area where millions rely on metro, bus and suburban rail lines which have been badly affected. Teachers, lawyers and medical staff have joined protests in which schools have been shut sporadically and flights have been grounded.

In an act of symbolism, the government held Tuesday’s talks in the same room where officials sat down with unions to find a way out of the May 1968 strikes.

French officials have appeared open to an offer by France’s largest union, the moderate CFDT, to hold separate talks on how to finance the pensions plan later, in order to end the deadlock over retirement age. The finance minister, Bruno Le Maire, said on Monday: “Never has a compromise seemed so close.”

The pension reforms were a key plank of Macron’s presidential manifesto – part of his promise to deliver what he has called the biggest “transformation” of the French social model and welfare system since the postwar era. In his New Year’s Eve address, he argued that he was not dismantling France’s social security safety net, but rather updating the deficit-plagued pensions system to ensure protections for future generations.

The leftwing CGT and Force Ouvrière unions have vowed to continue the strikes, including at refineries, and will lead a fresh day of mass walkouts and street demonstrations against the reforms on Thursday, which could see schools shut and public transport even more badly affected than usual, as well as another street protest on Saturday.