The militant group responsible for the threat has not been identified
Thousands of Nigerians have fled the Niger Delta oil town of Bonny after militants threatened to behead people who are not originally from the area.
The unknown group attacked soldiers in the town two weeks ago, killing nine people including a pregnant woman.
According to a newspaper article widely circulated by residents, the militants said they would return on July 16.
Bonny Island is home to a major oil and gas export terminal but production has not been affected.
Meanwhile, a militant attack in the Bonny Island area has left five people dead, the AP news agency reports.
About 30 militants attacked a Navy houseboat and three militants, a navy officer and civilian were killed, said Col Chris Musa.
In Bonny, youth leader Kingsley Adonis Pepple said people took the militant's threat seriously.
"They were handing out copies of this article to people in the street. There was panic. People packed up their entire family into a boat and fled."
Several boats had capsized and people drowned, he said, although there is no confirmation of this.
Mr Adonis Pepple said all the known militant groups in the area had denied issuing any threats.
He tried to tell people but they weren't taking any chances, he said.
The article said unnamed sources reported the militants' demand.
"Another source said that the hoodlums, after the face-off with the navy, entered town, shooting and giving ultimatum that all residents of the town who were from other places should leave the town before July 16 or risk being beheaded," the national Nigerian Tribune paper said.
The article was sent to many people in Bonny by family members begging them to get out before the deadline, Mr Adonis Pepple said.
Bonny is a city of over 100,000 people, many of whom work in the oil industry.
The new multi-million dollar Liquefied Natural Gas export terminal is nearby.
Shell announced on Tuesday that a pipeline leading to Bonny Island, attacked by militants two months ago, had been repaired and production resumed.
Militant attacks on oil infrastructure are partly responsible for Nigeria's oil exports being cut by around a quarter in recent years.
Militants have also kidnapped oil workers for ransom.
Some groups are demanding a larger share of the oil wealth, but others are criminal gangs who make a living from extortion and oil theft, Delta activists say.
Nigeria has seen several "communal crises" in recent years, in which one ethnic group attacks another seen as being "non-indigenous" to the area.
Hundreds of people were killed in Plateau state in 2004 in clashes between Christian militias and Hausa Muslims.
President Umaru Yar'Adua is meeting British Prime Minister Gordon Brown in London to discuss security issues in the oil-producing Niger Delta.
Mr Brown recently offered to help Nigeria bring an end to the violence and increase oil production.
Many in the region are afraid Mr Brown means to send military aid to the Delta.