Esmal Ali Sero, head of the Afar administrative region, said about 25 Eritrean "commandoes" kidnapped the British citizens along with their Ethiopian drivers and translators on Thursday night. He cited local investigators.
A senior Ethiopian official in the ruling party, who asked not to be named, also said Eritreans were behind the kidnapping.
Earlier on Saturday, a team of British officials arrived in Ethiopia to help in the hunt for the missing group. The foreign office in London would provide no further information on its efforts.
Margaret Beckett, the British foreign secretary, on Friday confirmed that five "members of staff, or relatives of members of staff, at the British embassy in Addis Ababa" were missing in the desert region which borders southern Eritrea.
On Saturday, a team of British officials arrived in Ethiopia to help in the hunt for the missing group.