PARIS (Reuters) - Pirates off the coast of Nigeria kidnapped six Russians and an Estonian during an attack on their ship on Monday, the French company operating the vessel said on Wednesday.

Another nine crew members were safe after the ship reached the Nigerian port of Onne in the oil-rich Niger Delta, said a spokeswoman for Bourbon, which supplies vessels to the offshore oil industry.

Pirate attacks are on the rise in the Gulf of Guinea, which is second only to the waters around Somalia for piracy.

Attackers usually seize boats to steal their cargo then free the crew. Kidnappings for ransom also take place in the waters around the delta, the heart of Africa's biggest energy industry.

Pirates freed a Greek-operated gasoline tanker earlier this month that they had hijacked in the Gulf of Guinea near Ivory Coast. Fuel ships are a favorite target.

In August pirates attacked a Greek-operated oil tanker with a crew of about 20 off the coast of Togo. They released the ship a few days later after stealing 3,000 tonnes of fuel.

Nigerian navy spokesman Commodore Kabir Aliyu said his forces were searching for the pirates involved in Monday's attack.

(Reporting by Patrick Vignal; Additional reporting by Tife Owolabi in Yenagoa; Writing by Tim Cocks; Editing by Andrew Heavens)