The company said the remains of three unidentified crew members were discovered on board the vessel which continues to be on fire in the Arabian Sea.
"Given the time passed and the severe fire damage of the vessel, we must conclude by now that we have lost all four colleagues who have been missing since the fire," the Copenhagen-headquartered company said in a statement.
"Our most heartfelt condolences go out to the families of our deceased colleagues. We share their sorrow and do our utmost to support them in this devastating time," said Chief Operating Officer Soren Toft.
'Maersk Honam' caught fire around 390 nautical miles off the Agatti island in Lakshadweep last Tuesday while sailing from Singapore to Suez. It had a crew of 27, who decided to abandon the ship after failing to contain the blaze.
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While 23 crew members were rescued immediately by passing merchant vessels, fate of the remaining four was unknown till now.
Inability to find them at sea after exhaustive searches had resulted the Indian Coast Guard, which was coordinating both the fire fighting and search and rescue operations, to speculate that the four would have been stuck on board.
The missing Indian national is identified as Sadik Hegde, a cook.
"Our colleagues who were evacuated to local hospitals in varying conditions of health are improving and we are now preparing to bring them back to their families as (and when) their condition allows," said Chief Technical Officer Palle Laursen.
A majority of the crew members were released from hospitals in Kerala, while the rest were moved to general wards from intensive care units due to improvement in their condition, as per the statement.
The vessel, with a capacity to carry 15,000 standard 20-footer containers, was carrying over 12,000 20-footer equivalent cargo, some of which were earmarked as "dangerous".
While the exact cause for the fire was still unknown, the company confirmed that the blaze originated in the cargo near the sailors' quarters.
The company said on-board firefighting efforts were progressing with specialised vessels being engaged in the operation.
The company said it would conduct a full investigation to determine the "cause of the fire and the impact to the vessel and cargo.
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