On the political front, the Gulf Cooperation Council (GCC) reiterated its support for Yemen's beleaguered president, as militiamen opened fire to disperse thousands of his backers demonstrating in Sanaa.
Unidentified gunmen seized 30-year-old Isabelle Prime -- a consultant working on a World Bank-funded project -- and Sherine Makkaoui from a car in the capital on Tuesday.
French Foreign Minister Laurent Fabius said Paris was making "every effort" to reach Prime's kidnappers, while the abducted Yemeni's family said contacts have been made with tribal chiefs and the Shiite militia known as Huthis.
"We have also contacted, for the same reason, the interior ministry and the Huthis."
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The employer of the two women, Francisco Ayala, president of Ayala Consulting, said their wherebouts, the identity of the kidnappers and their demands remained unknown.
The interior ministry, leading the search with help from Ayala's local security advisers, "are telling us that they are working on the case... But we don't know anything concrete as yet," he told AFP from Ecuador.
After the Huthis' attempts to expand into southern and central Yemen were checked by fierce resistance from Al-Qaeda and from Sunni tribesmen, the militia moved to take power this month in what Yemen's Gulf neighbours branded a coup.
Prime and Makkaoui were seized after their car was stopped by men dressed as police, their employer said.
Western nations including Britain, France and the United States closed their embassies in Yemen this month over security concerns and have urged their citizens to leave.
But a US photojournalist and a South African teacher held by Al-Qaeda were killed during a failed American rescue mission in December.