In a statement, the Italian line said: "The security of our guests and crew is Costa Crociere's priority and a necessary condition for calm and pleasant vacations."
Alternative ports are being worked out, it said.
Costa had a group of passengers in the Bardo Museum when the attack occurred.
Its 114,500-gt Fascinosa (built 2010) left port on Thursday morning, bound for Palma di Mallorca, with 13 passengers unaccounted for.
Nine