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BBCSix civilians and six soldiers were reported dead in the fighting in Shabwa province, east of the Yemeni capital.
The Ukrainian company has not been named. Reports say the local tribe had been pressing it to secure jobs for its members regardless of qualifications.
Many outlying areas of Yemen are prone to lawless behaviour by armed tribes.
Witnesses quoted by AFP said that the clashes began when tribesmen, angry that the oil firm had rejected their requests for employment, prevented staff from working.
Armed tribesmen set fire to a military vehicle and held six soldiers hostage for several hours before finally releasing them, they said.
Yemen is one of the world's poorest nations, despite lying in the world's richest oil-producing region.
It pumps about 350,000 barrels of crude a day, less than half of which is exported.
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