Beriziky told AFP: "My mission will be to bring the country back to constitutional order through free and transparent elections whose results will be accepted by everybody."
But although the new prime minister appointed was supposed to have been chosen by consensus, representatives of the exiled Ravalomanana refused to accept the choice and walked out of the ceremony.
"We refuse this appointment," chief Ravalomanana representative Many Rakotoarivelo said.
"In the roadmap it says that the prime minister cannot come from the same political grouping as the one supporting the president of the transition," he added, referring to the agreed arrangement for a return to democracy.
"You know that Omer Beriziky is a member of the Leader Fanilo party ... itself part of the group that used to back Rajoelina."
In mid-October most of the island's political players adopted a calendar to implement the so-called roadmap to new elections put forward by mediators from the 15-member Southern African Development Community (SADC).
The calendar provided for the naming of a new prime minister by November 1 at the latest, then the appointment of a transitional government and a parliament by November 17.
On November 30 the transition parliament is supposed to ratify the road map.
It was not immediately clear how the refusal of Beriziky by Ravalomanana's group would affect this calendar.
Some observers said that if Ravalomanana managed to place his supporters in other key posts then he might eventually accept Beriziky as prime minister.
Beriziky, who comes from the north of the island, served as ambassador to the European Union.
- AAP