The border dispute led to a two and a half year war and has raised concerns of a renewed conflict.
John Bolton, the US ambassador, told the Security Council that Jendayi Frazer, the assistant secretary of state for African affairs, and retired Marine-General Carlton Fulford, who directs the Africa Centre for Strategic Studies, would be travelling to the region "to discuss how to begin implementation of the demarcation process".
A December 2000 peace agreement that ended the border war provided for an independent commission to rule on the position of the disputed 1000km boundary, while UN troops patrolled a 24km buffer zone between the two countries.
But Ethiopia has refused to implement the international boundary commission's April 2002 ruling, which awarded the key town of Badme to Eritrea.
Angered at the international community's failure to ensure that the ruling is obeyed, Eritrea in October banned UN helicopter flights and vehicle movements at night on its side of the buffer zone.
In December, it ordered Western peacekeepers to leave the UN force monitoring Eritrea.
The Eritrea-Ethiopia border spat
led to a two-and-a-half-year war
The Eritrean government gave no reason, but the pullout demand came amid mounting concern that both sides were massing troops near the buffer zone as a prelude to a new war.
The UN called the Eritrean demands unacceptable but withdrew the American, Canadian, European and Russian troops.
Bolton announced the US initiative on Monday, at a closed-door Security Council meeting to discuss six options proposed by Kofi Annan, the UN secretary-general, for the future of the UN peacekeeping force, ranging from maintaining its present 4000-strong operation to withdrawing the entire mission.
The US ambassador said afterwards that he asked the council to freeze the current status of the UN force for 30 days "in order to bring some space for this diplomatic initiative and in order not to send any signals politically or otherwise that might complicate it".
Bolton said: "I made it clear to the council there were no promises, no guarantees ... but that we felt that this kind of diplomatic initiative could bring the movement on the underlying political dispute."
Augustine Mahiga, Tanzania's UN ambassador and the current Security Council president, said members were "very pleased" by the US initiative and had agreed to keep the force's status quo for 30 days to wait for the outcome.
Jean-Marie Guehenno, the UN undersecretary-general for peacekeeping, said there was a recognition "that everything has to be done to avoid increasing the risks on the front line between Ethiopia and Eritrea, and so time has to be given for diplomacy."
"Everything has to be done to avoid increasing the risks on the front line between Ethiopia and Eritrea, and so time has to be given for diplomacy"
UN Undersecretary-General for Peacekeeping
Guehenno, who recently returned from the region, said "there is a need for a real engagement by the international community."
He called the US decision to send a high-powered mission not only important but "essential".
"This is a very difficult mission. There is never a certainty of success. But I think it should be very much appreciated that the United States is prepared to take the diplomatic risk, to engage itself, to move the region away from war."
He said, the end goal must be the demarcation of the border and normalising relations between the two poverty-stricken countries so they can focus on development rather than spend money preparing for a possible war.