Ethiopia said it suspects the attack was linked to an African Union summit in Addis Ababa this month. It said the killings show that the international community "must now get serious about the destabilising role of the Eritrean regime in the region".
Gunmen in Ethiopia's north attacked a group of European tourists travelling in one of the world's lowest and hottest regions, killing five, wounding two and kidnapping two.
Ethiopia offered its condolences to the families of victims and said it would "do everything possible to try and get those taken prisoner released as soon as possible," a government statement said. "It is already clear that the attack was carried out with the direct involvement of the Eritrean government. There is a fear that the people who have been kidnapped might be taken across the border into Eritrea."
Ethiopia said the gunmen attacked the tourist group before dawn on Tuesday. Three Ethiopians were also taken hostage. Eritrea denied it was involved.
Austrian, Belgian, German, Hungarian and Italian nationals were among those in the tourist group, the Ethiopian communications minister, Bereket Simon, said on Wednesday.
Two Germans, two Hungarians and an Austrian were killed, according to an Interpol report cited by the spokesman for Hungary's prime minister. Two Belgians were seriously hurt and two Italians escaped unharmed, the report said. Two Germans were kidnapped.
Austria's foreign ministry confirmed that an Austrian man was among the dead. Germany's foreign minister also confirmed two German deaths. Germany's foreign minister said 12 other people were flown to safety by helicopter.
Those wounded in the attack arrived in Addis Ababa on Wednesday evening, where they were met by embassy personnel. A British diplomat at the airport said it was possible one Briton was among the group.
The tourists were visiting a volcanic region in Ethiopia's northern Afar region, which lies below sea level and is known for its intense heat and picturesque salt flats.
Some of the tourists appeared to be travelling with Addis Ababa-based Green Land Tours and Travel, according to three people in Ethiopia's capital.
Green Land Tours and Travel offers a 15-day travel package to the Afar region, which include visits to watch salt extraction from salt lakes and a trek around a volcano that spouts lava pools.
Some of the tourists on the trip also appear to have been booked by a company in Germany called Diamir, which posted a statement on its website saying that it deeply regretted what happened. Diamir said it had offered the Ethiopia trip several times a year since 2006.
"Up until the current incident, Diamir had no indications that the security of guests could be in question in the region," it said, adding that there was no German travel warning in place for Ethiopia, or parts of it, at the time of the incident.
Mr Bereket said that "some groups trained and armed by the Eritrean government" attacked the tourists about 20 to 25 kilometres from the Eritrean border.
Eritrea's ambassador to the African Union, Girma Asmerom, said Ethiopia's allegations are an "absolute lie" and that the attack is an internal Ethiopian matter.
The Austrian foreign ministry spokesman, Peter Launsky-Tiefenthal, said there was an Austrian foreign ministry travel warning in effect for the region since 2007 "because of several incidents involving attacks on tourist groups ... in some case politically motivated in others criminally motivated".