The French driver sustained a severe head injury when his car hit a mobile crane that was inside the trackside barriers to collect another car. He remains in a hospital in Japan.
The family statement was released by team Marussia, which will not race this week at the U.S. Grand Prix because of financial problems.
Bianchi's family says he "does indeed continue to fight" and wanted to thank his fans for their support. The family says doctors in Japan are in regular contact with neurosurgeons in Rome and the FIA medical commission and that they would continue to provide updates.