The 13 vessels included eight crude oil tankers and five refined oil tankers, APM, France's largest port, said.
Workers at the port of Marseilles will stage another 24-hour strike on May 9, which could hold up more tankers outside France's largest oil port of Fos-Lavera.
France's main union for port workers, part of the Confédération Générale du Travail (CGT), had last month called for weekly 24-hour strikes to protest against government reforms and proposed privatization.
The workers' union has indicated more strikes will come anytime during the period of May 14-21 - a move timed to coincide with the government's preparation to submit its reform legislation to the French senate on May 20-21.
Meanwhile, Marseilles's port director, Guy Janin, has been quoted as saying that Maersk Line had given notice that it would not call at the port's main Fos container terminal until the situation has 'stabilized'.
Reports this week said Marseilles is still reeling from the effects of the repeated strike action by port workers.