The date was set a year ago by the Ethiopia-Eritrea Border Commission, which was created following a bloody border war between the two countries.
The commission said it now considered the line it had drawn as the official border and its own mandate fulfilled.
Both sides say they accept the ruling, but neither has made any move towards implementing the recommendation.
Some 80,000 people died during the 1998-2000 war.
The commission has now dissolved itself but a small United Nations peacekeeping force (UNMEE) of 1,700 troops will remain in the border area until early 2008.
A UNMEE spokesman told the BBC it would do as much as it could to prevent hostilities between Ethiopia and Eritrea but said it would be unable to intervene should a new war break out.
The BBC's Elizabeth Blunt in Ethiopia's capital, Addis Ababa, says the commission can hardly be said to have succeeded, but its imminent disappearance leaves the two armies glaring at each other across a still unresolved border.
What was meant to be a demilitarised border is now thick with troops and bristling with weapons and representatives of the commission have not been able to get in to set up border markers, our correspondent says.
The two sides will not talk to each other and there is no obvious way to move the issue towards a more satisfactory conclusion, she says.
In the past few weeks there has been talk of UN involvement and perhaps the appointment of a facilitator to work with the two sides.
But so far no such initiative has been announced.
The Ethiopian and Eritrean leaders, Meles Zenawi and Isaias Afewerki respectively, were allies until after Eritrea gained its independence from Ethiopia in 1993.
Their rebel movements had fought together to overthrow long-time Ethiopian ruler Mengistu Haile Mariam.
The 1998-2000 war was ostensibly fought over the dusty town of Badme, which was subsequently awarded to Eritrea by the border commission.
But to this day the settlement remains under Ethiopian administration.
Meanwhile, Mr Meles has denied accusations made by separatist rebels in the south-east of Ethiopia that his troops have committed massive human rights abuses against civilians.
The rebel Ogaden National Liberation Front accused government forces of executing local residents during counter-insurgency operations in the region.
Mr Meles said such violations would not take place because his government respected human rights.
He said that given his own experience as a former rebel leader he knew that harassing civilians was the gravest mistake a government fighting an insurgency could make.