European nationals are among those killed, government official Berekat Simon said. He said Europeans were also thought to be among four people kidnapped in the attack.
The attack was carried out late Monday in the northern Afar region.
Afar is regarded as a haunt of both Ethiopian and Eritrean rebels.
Ethiopia and Eritrea have been bitter adversaries since their 1998-2000 border war.
Two other tourists were seriously hurt and a third is said to have escaped the attack unharmed, said Ethiopian Television (ETV).
It said the two injured tourists had been taken to a clinic by defense forces.
“The group of foreign tourists was attacked by gunmen late on Monday by members of a group that was trained and armed by the Eritrean government,” Ethiopian government spokesman Bereket Simon told Reuters.
“It is the usual terrorist activity by the regime.”
But an Eritrean official dismissed the accusation as baseless.
A Western diplomat also told Reuters that German nationals were among those killed, but that has not been confirmed.
However, reports in the German media said the tourists had been near the Erta Ale volcano.
Eritrea gained independence from Ethiopia in 1993 but the two countries soon became embroiled in border disputes.
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