The Sea Guardian consultancy said the Demeter "was attacked by pirates" at about 7:00 am (local time) on Saturday south of the Nigerian oil city, Port Harcourt.
"Pirates boarded the ship, kidnapped six crew, including (the) master, chief officer, second officer, second engineer, bosun and cook," it said on its website www.sguardian.com yesterday.
Reports suggested the attack was carried out by eight pirates in a black speedboat, it added.
The Demeter had been travelling from the capital of Equatorial Guinea, Malabo, to the Liberian capital Monrovia at the time.
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The MTI Network, a crisis communications firm that deals with incidents in the shipping industry, said the attack happened as the ship entered the port of Onne.
"All of the 12 remaining seafarers of the Demeter are safe and unhurt and the vessel has proceeded to safe waters," it said in a statement.
The Peter Doehle group said it would not disclose the nationalities of the crew members taken "for security reasons".
The International Maritime Bureau (IMB) has recorded 121 piracy incidents in international waters this year, including shootings, attempted kidnappings and hijackings of ships.
"The waters off Nigeria remain particularly risky," said the head of the IMB Pottengal Mukundan, pointing to the waters off the the state of Bayelsa, Bonny Island and Port Harcourt.
Mukundan said there had been an increase in reported hijackings and kidnappings, although many more had not been reported.
The IMB said "39 of the 49 crewmembers kidnapped globally occurred off Nigerian waters in seven separate incidents".
"Other crew kidnappings in 2017 have been reported 60 nautical miles (69 miles, 111 kilometres) off the coast of Nigeria," it added.