Eritrean officials have failed to meet the UN's top peacekeeper in Asmara to discuss the expulsion of peacekeepers.
Ethiopia has announced a troop withdrawal from the border
Jean-Marie Guehenno and his military advisor went to the Eritrean capital to try to end a ban on 180 western staff.
"The Eritreans indicated that they did not have much to say this time to us and they would not be meeting with Guehenno," a UN source told Reuters.
In Ethiopia, Prime Minister Meles Zenawi has accused Eritrea of escalating tensions along the border.
Eritrea has condemned the UN's "meddling" in the tense Horn of Africa.
It said Ethiopia's recent offer to pull back its troops from near the border was irrelevant.
The source said the UN team, who leave on Wednesday, were still hopeful that they would get a chance to talk to the Eritreans.
The BBC's Ed Harris in Asmara says the UN are anxious to keep open the possibility of meeting Eritrean officals and avoid any kind of confrontation.
The 10-day ultimatum for North American and European members of the UN Mission in Ethiopia and Eritrea (Unmee) to leave is being seen as an attempt to keep pressure on the international community to persuade Ethiopia to comply with an agreed border demarcation.
Whilst in Ethiopia on Monday, Mr Guehenno warned both countries of the dangers of a renewed border war.
Dec 2000: Peace agreement
Apr 2002: Border ruling
Mar 2003: Ethiopian complaint over Badme rejected
Sep 2003: Ethiopia asks for new ruling
Feb 2005: UN concern at military build-up
Oct 2005: Eritrea restricts peacekeepers' activities
Nov 2005: UN sanctions threat if no compliance with 2000 deal
A relocation of the affected troops is being considered, the UN says, but the expulsion order is unacceptable as it would set a precedent.
"We cannot accept [the exit order]. If you do, then you change the international character of peacekeeping," Unmee spokeswoman Gail Bindley-Taylor-Sainte told Reuters news agency.
The Horn of Africa neighbours battled over their border in a 1998-2000 conflict that led to some 80,000 deaths.
Under a peace accord, the UN deployed a peacekeeping force in a 25km buffer zone on the Eritrean side of the border and the two states agreed to accept the findings of the border commission.
But Ethiopia has not withdrawn its troops from the town of Badme, which the commission awarded to Eritrea.