An official from the Origins Ethiopia tour group told AFP news: "In the first convoy, there were 11 French, my guide, three drivers, a cook, two policemen.
"The other group had three British residents in Ethiopia, a cook, a guide, and two policemen."
He said he had lost contact with the guide accompanying the tourists on Tuesday night.
"A driver of one of my colleagues called me yesterday to inform me that one or two of my groups have been kidnapped," he said.
"The favour of Western countries is vital to the countries future"
Angus Hogg, Horsham, UK
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Ethiopia's government said it was aware of this week's incident, but could not confirm if it was a kidnapping.
"The government is monitoring the situation," an information ministry spokesman said.
The government requires all convoys visiting the area to have a minimum of two cars and travel with armed guards because of the threat of bandits.
In 1995, nine Italian tourists were captured by Afar tribesmen, then released two weeks later.
Afar separatists began a low-level rebellion against the Addis Ababa government in the 1990s, calling for the creation of a separate Afar state on territory which straddles Ethiopia, Eritrea and Djibouti.