A separatist militia group has threatened oil installations after the government arrested its leader and said it would charge him with treason, a capital offence.
The group has given the government until Saturday to release its leader.
Nigeria is the world's eighth largest oil exporter and the fifth main supplier to the United States, with a daily total output of about 2.5 million barrels.
Brigadier General Elias Zamani, a military commander in the delta, said on Friday the army was "on high alert," with stepped up patrols on water and land and from the air.
Hundreds of police reinforcements have been sent to the delta, but Zamani said the army had sufficient troops in the region for now.
"I can confirm that we shut down Robertkiri late yesterday, following information it was under imminent threat," said Chevron spokeswoman Edith Azinge in Lagos. She said the Robertkiri flow station usually produces 19,000 barrels per day.
Nigeria is the world's eighth
largest oil producer
With the move at Robertkiri, Chevron Corp. has now shut off 27,000 barrels per day of oil due to unrest in the Niger delta. On Thursday, militia fighters disarmed security forces guarding Chevron's Idama oil platform, forcing the company to stop production of 8000 barrels per day there.
A spokesman for Shell, which produces about half the oil pumped in Nigeria, said on Friday that the company had evacuated staff from some platforms in the Niger delta, but that production has not been affected. Many of Shell's oil facilities can run without staff.
The militia said on Wednesday it had overrun four Shell platforms, which Royal Dutch Shell PLC would neither confirm nor deny.
"We will unleash upon the government and its cohorts, violence and mayhem never before reported in the history of the Nigerian state," said a statement from the Niger Delta People's Volunteer Force on Friday.
The rebels say they attacked
four Shell platforms
A militia official threatened unrest in Port Harcourt, a major oil hub that was the scene of protests earlier this week. A security official said Chevron had evacuated its expatriate workers from Port Harcourt, but Chevron's Azinge would not comment on that.
The group is led by Moujahid Dokubo-Asari, who was arrested on Tuesday and appeared on Thursday before a court in the capital, Abuja. A judge ordered he remain in detention for two weeks before formal charges are brought.
Dokubo-Asari says his Ijaw ethnic group and the other people of the Niger delta should break away from Nigeria and take control of the billions of dollars of oil flowing from their land.
Police said Dokubo-Asari was arrested because he had called for the breakup of Nigeria in an interview published in Nigeria's Daily Independent newspaper. His lawyer, Uche Okwukwu, was also arrested after going to Abuja to secure his release, said Ariku Donalds, an attorney now representing both of them.
The unrest in Nigeria, along with growing demand and worries about spare capacity, has contributed to soaring world oil prices.
Disputes over oil have been causing bloodshed for years in Nigeria.
In 1995, writer Ken Saro-Wiwa and eight other activists from his Ogoni tribe were executed under the brutal regime of then dictator General Sani Abacha.
"We will unleash upon the government and its cohorts, violence and mayhem never before reported in the history of the Nigerian state"
Niger Delta People's Volunteer Force statement
They were hanged for the murder of four political rivals, but Saro-Wiwa's supporters say he was really targeted because he led protests against environmental damage by Shell.
In 2003, an ethnic revolt shut down 40% of Nigeria's oil output and killed at least 200. The following year, fighting involving the army and rival militias - including Dokubo-Asari's supporters - killed hundreds.
Human rights activists in the delta say Dokubo-Asari's militia is a creature of the government, alleging it was funded and armed by regional officials of President Olusegun Obasanjo's ruling party to help rig 2003 polls.
Obasanjo won the polls. There were widespread allegations from foreign observers of rigging in the delta.
Dokubo-Asari denies that he received any funding from the government.