Multinational oil companies have begun talks with Nigerian villagers who took over three oil installations on Sunday.
The Delta region holds the bulk of Nigeria's oil reserves
A spokesman said people from a remote Delta region community were protesting that they had been overlooked for jobs.
Such protests are common in the Delta region. Although the Delta region produces the bulk of Nigeria's crude oil, most people live in poverty.
The plants are run by the Nigerian wing of the Anglo-Dutch multinational Shell, and the US company ChevronTexaco.
"Our preference is for dialogue rather than a forceful end to the situation," a ChevronTexaco spokesman said.
"We are concerned for the safety of the occupiers and the employees and that is why we are appealing to them to vacate so that we can engage with them directly," he added.
A Shell representative said many of those who seized the platforms have now left them for talks.
"Most of the groups have now left the stations, but they left 20 invaders behind to ensure that we don't reopen the flow stations," said a Shell spokesman.
Early on Sunday morning, men and women from the Kula community in River state stormed at least three oil installations.
They closed down the Shell-operated Ekulama One flow station and then occupied the nearby Ekulama Two.
The Chevron-run Robert-Kiri flow station was also affected.
Chevron say they have arranged talks with Rivers state governor Peter Odili to look for a solution.
The lost production is estimated at about 90,000 barrels a day. Nigeria's normal daily output is about 2.5 million barrels.
The paramount ruler of Kula, chief Dan Opusingi, told the BBC by phone from Ekulama Two that his people had decided to stage the peaceful protest because they have been overlooked for jobs and development by the oil companies.
Last month, more than 80 protesters occupied a rig operated by Shell contractors in neighbouring Delta state and 17 people were injured when soldiers opened fire.
Journalists were later shown the graves of seven men who were reportedly shot dead in the incident, but the army denied that anyone was killed.