The leader, who uses the pseudonym Jomo Gbomo, said: "They have all been released within the last five minutes and are on their way to Port Harcourt."
There was no immediate confirmation of the release from the company or security agencies.
Gbomo said eight people were taken from the Mystras oil production vessel. Eni, the company operating the vessel, put the number of abducted at six, including one British, one Australian, one Polish, two Croats and one Romanian.
Power plant attack
In Thursday's second incident, 11 foreign workers and one Nigerian were kidnapped from a South Korean company's power-plant construction site.
A statement from Daewoo Engineering and Construction Co said an armed group broke into the company's facilities and drove the workers away in a stolen vehicle at 2am local time (01:00 GMT) from Afam power station, about 30km northeast of Port Harcourt.
The foreigners included eight Filipinos and three South Koreans, the company statement said.
Gunfire was heard during the 30-minute assault, a Daewoo official said.
|Tae-young, left, is among three senior Daewoo|
executives kidnapped on Thursday [EPA]
He said that no information was available on the plight of the workers and the kidnappers had not yet presented any demands.
A total of 1,755 workers, including 148 Koreans, were at the site, which has been guarded by Nigerian soldiers and security officials, Huh Hyon, a Daewoo spokesman, said.
The kidnapped Koreans include Chung Tae-young, a 52-year-old Daewoo managing director who was on a business trip to the area, and two senior Daewoo officials in Nigeria, he said.
Felix Ogbaudu, the Rivers state police commissioner, said a policeman was injured during the kidnapping.
Soldiers and police were searching for the attackers, officials said.
In the third incident, a Dutch man was kidnapped overnight from a bar in Warri, in southern Nigeria, a witness said on Thursday.
Flora Achudumoe, who owns Flora's bar near an oil company compound in the city centre, said the man was an unemployed oil worker and was taken by a group while he was watching football on Wednesday night.
Attacks and kidnappings of this kind are common in Africa's largest oil producer, where anti-government fighters and criminals use them as leverage against the government or to extract payment.