The Southampton-based firm said it is working with government and industry bodies to enforce safety measures on its ships.
Those who booked cancelled trips will received a voucher which gives an additional 25% on top of the amount paid for the holiday.
Carnival announced last month that many of its cruise brands would not sail until late this year or 2021.
Costa and AIDA Cruises are paused until 31 July, while all Europe, Canadian and Alaskan cruises for its Holland America line were cancelled for 2020.
Princess Cruises will not run throughout the summer, with some that had been planned for autumn around Japan, Australia, Hawaii and French Polynesia cancelled too.
The ‘ultraluxury’ Seabourn brand is planned to resume in October and November.
Shares were flat at 1,130.02p on Tuesday before close.