Both Horn of Africa nations have been massing troops near the border and Eritrea has been restricting the work of UN peacekeepers, raising fears of a reprise of their 1998-2000 war for territory.
UN Undersecretary-General for Peacekeeping Jean-Marie Guehenno was dispatched to the region this week by UN Secretary-General Kofi Annan.
Eritrea's order last week for 180 US, Canadian and European staff of the UN peacekeeping mission that monitors the border to leave by Friday has created a "crisis", Gail Bindley-Taylor Sainte, spokeswoman for the UN mission in the two countries, said by telephone from Eritrea's capital, Asmara.
"The under secretary-general has decided to extend his visit because of the importance of the situation on the ground," she said on Wednesday.
The UN mission also delayed plans to start withdrawing staff affected by the expulsion order on Wednesday.
The UN Security Council was expected to meet later on Wednesday in New York to discuss "all options" for the peacekeeping mission - including its withdrawal, Sainte said.
The nearly 3300-strong peacekeeping force is composed of peacekeepers and military observers from 40 countries.
The largest contingent, with more than 1500 troops, is from India.
On Tuesday, Ethiopia's Prime Minister Meles Zenawi said his country needed to maintain enough troops on the disputed border to keep Eritrea from starting a new war.
"In this respect we have to show that there is proportional force and, until a lasting peace has been secured, this will continue"
Prime Minister of Ethiopia
"In this respect we have to show that there is proportional force and, until a lasting peace has been secured, this will continue," Meles said, a day after the fifth anniversary of a peace deal that has failed to resolve the border dispute between the Horn of Africa two nations.
Eritrea gained independence from Ethiopia in 1993 after a 30-year guerrilla war, but the border was never agreed on and new fighting broke out in 1998.
The 1998-2000 war for territory claimed tens of thousands of lives and cost both countries - two of the world's poorest - an estimated $1 million a day.
An international commission set up under a 2000 peace agreement determined a border, awarding the key town of Badme to Eritrea.
Ethiopia has yet to withdraw from Badme, and Eritrea accuses the international community of shirking its responsibility to ensure the demarcation ruling is obeyed.
In recent months, both countries have been massing troops near the border, and Eritrea has been restricting the work of UN peacekeepers.
The UN estimates that since December, Ethiopia has moved around eight divisions - about 50,000 men - and tanks, missiles and other military hardware to the border.
Some 380,000 troops have
massed along the disputed border
Diplomats estimate around 380,000 troops are entrenched along the 1000km frontier - around 130,000 on the Ethiopian side and 250,000 on the Eritrean side.
On Saturday, Ethiopia's Foreign Minister Seyoum Mesfin announced it would pull back troops in compliance with a UN order.
As of Tuesday, there was no confirmation the pullback had begun.
On 5 October, Eritrea banned helicopter flights by UN peacekeepers in its airspace in a buffer zone with Ethiopia.
It then banned UN vehicles from patrolling at night on its side of the zone, prompting the UN to vacate 18 of its 40 posts.
Despite repeated appeals from the Security Council and secretary-general, Eritrea has refused to lift these restrictions.
Last month, the council passed a resolution warning of possible sanctions unless Eritrea lifts restrictions on the UN peacekeepers and the two sides reverse the troop build-up.
Ethiopia was told it could face sanctions unless it pulled back in accordance with the border demarcation.