Three bodies have been recovered and nine victims are still missing after the collision off Mangalore of a CMA CGM containership and a fishing vessel earlier this week.
A company spokesman told TradeWinds the 10,106-teu APL Le Havre (built 2012) has not been detained and all crew remain on board.
The spokesman denied reports that the master is in custody, adding that nothing is known about how the expected casualty investigation will proceed.
The crew of the APL Le Havre are credited with recovering two of the 14 crew members of the fishing boat, identified as the IFB Rabah.
Indian media reports said the boxship collided with the fishing boat in the early hours of 13 April.
'Deep concern'
In a statement, CMA CGM Group said it was "deeply concerned about the situation and about reports of a number of fatalities and missing crew members from the fishing vessel".
"The vessel remains on site, and the company and crew continue to work with the Indian coastguard, relevant authorities, and local vessels in the ongoing search and rescue operation," CMA CGM said. "APL Le Havre crew and CMA CGM are cooperating fully with the authorities in their investigations."
The company underscored that the APL Le Havre's master "immediately initiated emergency response procedures with Indian authorities".
It added: "Despite severe weather conditions, two fishermen were recovered from the water by the crew of APL Le Havre."
The APL Le Havre was bound from Singapore to Mumbai at the time of the collision. The ship is financially owned by China Construction Bank Financial Leasing and has protection and indemnity cover with Gard.