The attack marked a sharp deterioration in already deeply troubled relations between the two Horn of Africa countries and raised the risk of an Eritrean counter-strike, said one analyst.
There was no immediate reaction from Eritrea.
Ethiopia's government said it would continue to take "measures" for as long as the Eritrean bases were used as bases for cross-border attacks by rebels, an accusation Asmara has dismissed in the past.
"Our national defence force has today taken measures against military posts inside Eritrea in which subversive and anti-peace elements were trained," government spokesman Shimeles Kemal told reporters.
Ethiopian soldiers attacked three locations - Ramid, Gelahbe and Gimbi - 18 km (11 miles), 16 and 14 km respectively inside southeastern Eritrea, he said.
Shimeles said Eritrea had been uses its bases to train an Ethiopian rebel group that killed five tourists and kidnapped two others in Ethiopia's remote Afar region on Jan. 17. He also blamed the rebel group for the kidnapping of a group of Westerners and their guides in the same region, which borders Eritrea, in 2007.
"These groups are operating in the Afar area. We know for certain that the Eritrean government harbours, supports, trains and deploys subversive groups that occasionally launch attacks on civilian and infrastructure targets inside Ethiopia," Shimeles said.
"We will continue our measures as long as they remain a launching pad for similar attacks," he added.
Rashid Abdi, an independent Horn of Africa analyst, told Reuters Thursday's attack could lead to a "major confrontation" between the two countries.
"The Eritreans will likely respond back, and my hope is that the Americans and the EU will step in now to diffuse the situation," Abdi added.
A bitter dispute over the position of Eritrea and Ethiopia's shared border was not resolved at the end of the 1998-2000 war.
The Hague-based Eritrea-Ethiopia Boundary Commission ruled in 2002 that the border village of Badme belonged to Eritrea.
However, the village remains in Ethiopia and Eritrea blames the international community, and the United Nations in particular, for not forcing Ethiopia to accept the border.
Tensions along the frontier rose sharply in November 2005 as both countries moved up troops. By January 2006, Ethiopia had complied with a U.N. demand to withdraw its soldiers.
The United Nations has also slapped sanctions on Eritrea, accusing it of supporting Islamist rebels in Somalia, a charge the Red Sea state strongly denies.
Despite the repeated denials that it is not a destabilising force in the volatile Horn of Africa region, Eritrea is widely regarded in the international community as a pariah state and is deeply mistrusted by its neighbours.
Eritrea accuses Ethiopia - Washington's main ally in the Horn of Africa - and the United States of influencing a U.N. monitoring group with fabricated evidence about the reclusive Red Sea state's links to militants in Somalia.
Gunmen killed two Germans, two Hungarians and an Austrian in a dawn attack on a group of tourists in the remote Afar region on Jan. 17, and seized two Germans and two Ethiopians.
A rebel group in the Afar region said last week it had freed the two Germans, although there has been no official confirmation of the release.
Air traffic networks across SA modernised
24 May 2013 - Thales and Air Traffic Navigation Services (ATNS) Company of South Africa longstanding partners in air traffic management (ATM) systems are immensely proud to announce the recent signature of several significant ...
defenceWeb shines at Air Capability Demonstration
21 May 2013 - defenceWeb, Africas leading defence and security news portal, was invited by the South African Air Force to attend its annual Air Capability Demonstration a spectacular live-fire showcase of the ...
Airbus Military, EADS North America deliver HC 144A Maintenance Training Unit to US Coast Guard
16 May 2013 - The US Coast Guard Aviation Logistics Center has purchased the prototype CN235 aircraft and plans to transform it into an HC-144A maintenance training unit. The HC-144A is based ...