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Massoel Shipping said its bulk carrier MV Glarus, with 19 crew, came under attack early Saturday morning as it transported bulk wheat from Nigeria's commercial capital Lagos to the southern oil hub of Port Harcourt.
"Having destroyed much of the vessel's communications equipment, the criminal gang departed taking 12 of the 19 crew complement as hostage," it added.
Massoel spokesman Patrick Adamson told AFP it was the second largest number of people taken from a ship in the oil delta southeast of Nigeria this year.
"Pirates usually don't make contacts in the first 48 hours, so we don't have any news on that," he added.
For safety reasons, neither the identities nor nationalities of the hostages would be released, he said.
More than 60 crew were reported kidnapped last year in waters off Nigeria, Africa's leading crude producer, although many attacks are not reported.
The Geneva-based shipping company said "all the appropriate authorities have been notified" and specialists have been called in to "secure the speedy and safe release of those being held."
"Families are being kept closely informed of the situation."
Switzerland's foreign ministry said it "has been informed of the attack on Glarus, a vessel sailing under a Swiss flag along the Nigerian coast."
The Swiss Maritime Navigation Office was in contact with the vessel's operator, it added.