In the 21-second tape posted on YouTube, Prime is shown seated on the ground dressed in black and appeals to the French and Yemeni presidents to take action to secure her release.
Prime, a 30-year-old woman working for the World Bank, was captured in late February by unidentified gunmen in the Yemeni capital.
She was taken by six men dressed as policemen, while her driver escaped.
The woman was seized with her translator Sherine Makkaoui, who was later freed in the southern city of Aden on March 10th.
There has been no word on the identity of Prime's kidnappers.
Yemen has descended into chaos since Shiite Huthi militia swept into Sanaa from their mountain stronghold in the north last year, eventually prompting the president and prime minister to resign.
(In March, Yemeni women took part in a rally calling for Prime's release. Photo: AFP)