Three Australians and a New Zealander are among seven men taken by a group of armed men, who killed one of their drivers.
The Niger Delta is oil rich but has been plagued by unrest for decades.
A four-vehicle convoy was reportedly travelling to work on Wednesday from the regional capital Calabar to the United Cement Company of Nigeria when it was ambushed.
The ambush occurred around 5.30am while they were crossing the Idundu Bridge, a 220-metre stretch of concrete.
One driver was killed, but Foreign Minister Julie Bishop says two other people managed to escape, including one Australian.
"The details of this are still being investigated. We have some understanding of what occurred, but I won't go into too many details lest it affect the outcome."
Diesel mechanic Tim Croot got away, reportedly by hiding under the truck in the pre-dawn dark.
Witnesses say the others were bundled onto a waiting boat, with some describing up to 30 attackers involved in the kidnapping.
Prime Minister Malcolm Turnbull has described the situation as serious.
"In many respects, the less Julie (Bishop) and I say about this, the better, from the point of view of recovering the kidnapped people, okay? But it is a very serious kidnapping, a very serious criminal assault. One person was killed, as you know, and seven people kidnapped."
Three are Australian, employees of the Perth-based mining firm Macmahon, contracted to provide services to the United Cement Company of Nigeria.
The men have been identified locally as engineer Jack Couranz, project manager Mark Gabbedy and 58-year-old Peter Zoutenbier from Queensland.
Mr Couranz had reportedly joined the company straight out of university, and Mr Gabbedy had reportedly worked in Nigeria for over a year.
Mr Turnbull says the government is still waiting for further information.
"We are working with the authorities, the local authorities, at the highest levels. We don't know, at this stage, the identity of the kidnappers. The families in Australia have been notified, of course."
The other kidnap victims have been identified as Jamal Khan from New Zealand, Wayne Smith from South Africa and two Nigerian colleagues.
There have been conflicting reports on the names of the two Nigerians.
When asked if the New Zealand government would pay a ransom if one were demanded, Prime Minister John Key was unequivocal.
"In the case of the government, no. Our very strong policy is to not pay ransom. And the reason for that is that we think, if we paid a ransom, we potentially put a bounty on the head of any New Zealander who travels to a dangerous part of the world."
Newly appointed Nigerian state police commissioner Jimoh Ozi-Obeh says he is confident of the men's safe return.
He says authorities are working with the Nigerian navy and will ensure the men are released unharmed.
The local government has been trying to encourage investment in the area, but security remains an issue, with plunging oil prices fuelling discontent.
There have been 30 kidnappings over the past year for lucrative ransoms.
Local authorities have made moves to stop the kidnappings, signing a bill into law last year so convicted kidnappers could face the death penalty.
Macmahon has confirmed the latest incident, saying it is working to ensure the safe return of all the men involved.
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