An EU delegation is visiting Eritrea to try to boost the flagging peace process with Ethiopia.
Badme is still a sticking point in the peace process
Irish Foreign Minister Brian Cowen, who leads the group, will hold meetings with the two countries' leaders on Monday and Tuesday.
He said the visit would give a strong message for the two sides to move the process forward.
Peace efforts stalled when Ethiopia rejected a ruling that a disputed town, Badme, was in Eritrean territory.
But the UN has agreed to keep peacekeepers on the border to support the 2000 ceasefire.
Mr Cowen, whose country holds the current EU presidency, is backing UN efforts to resolve the dispute.
"The visit shows an interest and we would expect they would bring something tangible to move the process forward," said Eritrean presidential spokesman Yemane Gebremeskel.
Eritrea insists that the border ruling must be implemented and its leaders refused to meet UN special envoy Lloyd Axworthy in February because they thought he was seeking a different solution to the dispute.
Mr Cowen said he would encourage both sides to work with Mr Axworthy.
He will hold meetings with Ethiopian officials on Tuesday, before flying to Rwanda on Wednesday to attend ceremonies marking the 10th anniversary of the genocide.