"Three Chinese nationals were abducted by some unknown gunmen within the early hours yesterday," a senior police officer told AFP, requesting anonymity.
He said the gunmen had stormed a quarry outside Lokoja, the capital of Kogi state, and engaged the policemen on guard in a shootout.
"One policeman was killed while another sustained gunshot wounds," he said.
He said the assailants escaped with their hostages on foot through the bush, adding that police were on their trail.
It was unknown whether the kidnappers were planning to demand a ransom.
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Two weeks ago, two other Chinese nationals were kidnapped in the state, while an American missionary was taken from her school last month.
The missionary, who works in the village of Emiworo where her Free Methodist Church runs a community organisation, was released last week.
State police said they were unaware of any ransom paid for her liberation.
Foreign nationals have often been kidnapped in Nigeria by local gangs who typically release hostages following a ransom payment.
Such abductions are especially common in the southern, oil-producing Niger Delta, where expatriates working with large oil companies have been a frequent target.
A number of people seized by Nigerian Islamists have been killed by their captors, while others have died during botched rescue operations.