Officials say MV Seaman Guard Ohio was detained on 12 October by the Indian Coast Guard and is currently anchored at a port in southern Tamil Nadu state.
Its 35-member crew include Indians, Britons, Ukrainians and Estonians.
The ship’s owner, AdvanFort, said the vessel was involved in supporting anti-piracy operations in the Indian Ocean.
But there have been differing accounts of the chain of events from the Indian authorities and the US-based security firm.
The Indian authorities say they intercepted the American ship last weekend when it was reportedly sailing off the coast of Tamil Nadu.
Police also said they found weapons and ammunition on board, which had not been properly declared. Officials say the vessel was not authorised to carry arms in Indian waters and that it never produced the necessary paperwork.
But in a statement released on Monday, AdvanFort said India’s coast guard and police allowed the vessel to enter the port to refuel and shelter from a cyclone which hit India’s eastern coast last weekend. The company even thanked officials.
It added that all weaponry and equipment on board was properly registered.
In recent years piracy has emerged as a major threat to merchant ships in the Indian Ocean and the Arabian Sea, with ships and their crews sometimes hijacked for ransom.
There have been fewer attacks recently, partly because more armed guards are now deployed on board.
On Friday, police said that 33 crew members had been taken to a local police station for questioning. Two had been allowed to remain on the vessel in port at Tuticorin.
Six of the crew members are Britons and the British high commission in Delhi said consular officials had been in touch with them by email and with the local authorities, but they were still trying to clarify exactly what had happened and on what grounds they had been detained.
The US embassy told the BBC it had “no comment” to make.
According to AdvanFort there were privately contracted security personnel on board the Sierra-Leone registered MV Seaman Guard Ohio.
It said that as these men routinely provide counter-piracy protection they also had uniforms, protective equipment, medical kits, rifles and ammunition – “all of which is properly registered and licensed to AdvanFort”.
The company added that the vessel “provides an accommodations platform for AdvanFort’s counter-piracy guards between transits on client commercial vessels transiting the high risk area”.
Analysts say that anti-piracy measures on high-risk shipping routes are poorly regulated and India is increasingly sensitive to violations of its maritime boundaries.
India directly supports the multi-national campaign to combat the mostly Somali pirates targeting ships in the Indian Ocean with its own navy.
But it’s been controversial too, with the Indian authorities prosecuting two Italian marines on anti-piracy duty for allegedly shooting two fishermen inside Indian waters last year.
They were guarding an Italian oil tanker and said they mistook the fishermen for pirates.