On Wednesday the army deployed more troops to the area and oil companies tightened security around their offices.
Heavily armed men stormed the headquarters of Italian oil firm Agip on Tuesday, killing eight policemen and one civilian, and robbing a bank on the premises.
Return Powei, from the village of Ogbotobo, said: "There are soldiers everywhere and I don't want my three girls in the line of fire. Our youths run into the forest when they hear the soldiers are coming. Everyone is moving out of Ogbotobo."
It was not clear if Tuesday's attack on Agip, a unit of Italy's ENI, was the work of the Movement for the Emancipation of the Niger Delta (Mend), whose campaign of sabotage and kidnapping has helped push world oil prices to four-month highs.
Mend pledged on Wednesday to make Royal Dutch Shell suffer unless it pays $1.5 billion to delta villages in compensation for decades of oil pollution.
The government has so far shown restraint in dealing with the militants.
It has set up a committee to negotiate the release of four foreign oil workers kidnapped on 11 January - an American, Briton, Bulgarian and Honduran - but it appears to be making little progress.
"Shell will suffer more damages and losses than it can hope to pay as compensation. Any foreigner who decides to remain in the Niger Delta will have himself only to blame"
Email statement from Mend
At the riverside in the delta city of Warri, villagers arrived in boats packed with household possessions, fearful of possible military attacks to avenge the killing of a dozen soldiers in a raid on a Shell oil platform on 15 January.
Shell has already withdrawn 500 staff and cut its output by 221,000 barrels a day.
Hundreds of contractors have also fled the area as the military deploy extra troops to platforms across the vast region of mangrove swamps and tidal creeks.
Oil unions have threatened to pull out completely from the delta, which produces almost all Nigeria's 2.4 million barrels a day, if security deteriorates further.
ThisDay newspaper, reported on Wednesday: "There is palpable fear in the air that another Odi is in the making."
The paper was referring to a 1999 raid when rights groups say troops killed hundreds in the delta village of Odi to avenge the killing of 12 policemen.
The militants said in an email to Reuters on Tuesday they had not started talks for the release of the four hostages who were taken from an offshore oilfield operated by Shell.
The email from the group, seeking the release of two Ijaw leaders and $1.5 billion from Shell to compensate villages, said: "The hostages are in good health ... and are going nowhere for as long as our demands are not met.
The militia group is demanding
Alamieyeseigha's (C) release
"Shell will suffer more damages and losses than it can hope to pay as compensation. Any foreigner who decides to remain in the Niger Delta will have himself only to blame."
Nigerian secret agents have arrested three men they say are closely linked to the kidnappers, but the militants distanced themselves from the detainees, saying they were profiteers looking for a share of any ransom.
The email said: "We gather these people were arrested for being unable to provide the hostages after they were paid. The hostages were not being held for money."
The group said the captives will be freed only in return for the release of Mujahid Dukubo-Asari, a militia chief, and Diepreye Alamieyeseigha, a former Bayelsa state governor who was impeached for money laundering last month.