"We are able to accept bookings again," the company said on its website.
In addition, "the majority of our terminals are now operational. Some of these terminals are operating slower than usual or with limited functionality."
Maersk said on Wednesday that a number of its 76 container terminals were affected by the cyberattack and were forced to run on manual systems, but would not specify which sites.
"We continue to assess the situation. Until this analysis is complete, we cannot be specific about how many sites and locations are affected or when normal business operations are restored," today's statement said.
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Maersk's statement Thursday stressed that all of its vessels "continue to be under control, employees are safe and communication to crew and management onboard is functioning."
The series of cyberattacks began in Russia and Ukraine on Tuesday, hitting government and corporate computer systems across the world as the virus spread to western Europe and across the Atlantic.
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