Cameroonian President Paul Biya ordered tight security measures and urgent steps to free the hostages, who include four children. They were kidnapped by armed gunmen in the country's far north on Tuesday and whisked toward Nigeria. A ministry statement said the Cameroonian government is in contact with Nigerian and French authorities.
Officials suggested the involvement of Boko Haram, one of Nigeria's Islamic extremist sects.
Nigeria's borders were also put on red alert in the hunt for the kidnappers believed to be in the country or heading to the country, said Nigeria's comptroller general of immigration, Rilwan Musa.
"We have already sent alert messages across the northeast borders and all other borders of the nation," he said. "We have told our men to be on the alert. We have given the border posts all the supports they need to tackle them whether in the day or at night."
The kidnapping came as thousands of French troops are deeply involved in a military intervention against Islamic extremists who had taken control of a big part of the West African country of Mali.
French President Francois Hollande, speaking at a Cabinet meeting Wednesday, called it an "odious act" and expressed particular horror that children were involved, according to his government spokeswoman.
Speaking in parliament Wednesday, French Foreign Minister Laurent Fabius said: "We must do the utmost to free our hostages, but nothing would be worse than giving in."
Meanwhile, in France, spokeswoman Agnes Thibault-Lecuivre of the Paris prosecutors office, says it has opened a preliminary investigation into "kidnapping and sequestration by an organized group in relation with a terrorist organization" following the hostage-taking. France's counterterrorism agency DCRI is in charge of the probe, she said Wednesday.
France's BFM TV reported that a French helicopter had left a French military base in Tchad toward northern Cameroon, and two operatives with France's DGSE spy agency have traveled to the region. French military officials declined to comment to the Associated Press about that.
France said Wednesday that there was no proven link between the French operation in Mali and the Cameroon kidnapping. But, speaking on France-2 television, Defense Minister Jean-Yves Le Drian said: "These are groups who adhere to the same fundamentalism and who have the same methods, whether it is in Mali, in Somalia or in Nigeria, who want to create a lawless zone" stretching from the Atlantic across the southern edge of the Sahara to Sudan.
France's government warned French citizens to avoid travel in northern Cameroon after the kidnapping and urged anyone currently there to leave immediately.
French Foreign Ministry spokesman Philippe Lalliot, in an online exchange with reporters Wednesday, said that in northern Cameroon, "There was never a security incident linked to terrorism; Nigerian terrorist groups had never carried out actions in this part of Cameroon."
A Cameroonian government official said military helicopters were being used in the search.
The French gas group GDF Suez identified the captives as an employee working in Yaounde, the Cameroon capital, and his family. French media say the children are between 5 and 12 years old.
Cameroon state television cited government sources in the locality as saying that the three adults have been separated from the four children.
The family was on tour at the Waza National Park in Cameroon's Far-North Region before it was abducted at gunpoint by five gunmen aboard motorbikes, according to paramilitary sources in the area.
A Cameroon government statement late Tuesday night said the hostages were abducted at Sabongari, seven kilometers (four miles) from Dabanga, which flanks Cameroon's frontier with Nigeria. The statement did not say whether the Cameroon government is in contact with the kidnappers.
Associated Press reporters Haruna Umar in Maiduguri, Nigeria, and Angela Charlton in Paris contributed to this report.