High-speed TGV services, notably those heading to Spain and Italy, have been reduced to one in three trains at the start of France's main tourist season. Visitors arriving at Paris's international airports also faced disruption getting into the city.
Thierry Lepaon, the head of the CGT trade union — the largest representing rail workers — urged President Francois Hollande to resolve the crisis by the weekend as Valls appealed to the strikers' "sense of responsibility".
The head of the moderate CFDT union, Laurent Berger, on Saturday called for a halt to the strike which he said was causing "too many people to sweat".
The action takes place just one week before France's lower house of parliament examines proposed reforms aiming to tackle the rail sector's soaring debt.
Cuvillier said Tuesday the sector's debt stood at more than €40 billion ($54 billion), and would likely soar to €80 billion by 2025 if nothing was done to stem it.
The unions behind the strike say the proposed reforms will not help rein in the debt.