The UN has already withdrawn most of its peacekeepers from Eritrea
The UN Security Council has voted unanimously to end its peacekeeping border mission to Ethiopia and Eritrea.
The UN withdrew most of its 1,700 peacekeepers in February after Eritrea withdrew its support for the mission.
Eritrea wanted the international community to make Ethiopia comply with an international border ruling.
Meanwhile, in discussions to extend the UN mandate in Darfur, some members are pushing for war crimes charges against Sudan's leader not to be pursued.
The BBC's Laura Trevelyan at the UN says the vote ending the Eritrea-Ethiopia mission is formally recognising the reality on the ground.
But there is concern within the UN that the move will encourage other
governments to drive out peacekeepers, she says.
In April, UN Secretary General Ban Ki-moon warned of a possible return to war if the peacekeepers pulled out of Eritrea and Ethiopia.
Before the vote, Ethiopian Prime Minister Meles Zenawi said he thought that unlikely to happen.
"The peacekeepers played an important role, but one cannot say that their role was irreplaceable in the sense of maintaining the relative peace along the borders that we now have," he told the BBC's Focus on Africa programme.
"So the risks will naturally be increased. But I don't think the fact that the peacekeeping operation is finally terminated will mean that war will start again."
BBC Africa analyst Martin Plaut says the war between the two neighbours that erupted in 1998 was the largest conventional conflict to have been fought on the African continent since the end of the Second World War.
Tanks, heavy artillery and modern aircraft were thrown into the fray and tens of thousands of people died in two-and-a-half years of bitter trench warfare.
The forces of the two nations are now separated by a few hundred metres.
The UN withdrew most of its peacekeepers after Eritrea cut off fuel and food to the UN mission last year.
It was angered by Ethiopia's refusal to comply with a binding ruling from international arbitrators that awarded disputed territory to Eritrea.
Ethiopian troops are stationed deep within the territory given to Eritrea, and Eritrea had demanded that the UN compel Ethiopia to withdraw.
However, our correspondent says there was no appetite at the UN for such direct intervention.
With regard to peacekeeping efforts in Sudan, South Africa's ambassador to the UN, Dumisani Kumalo, says an increasing number of countries want the International Criminal Court to delay its moves to indict Sudan's President Omar al-Bashir.
South Africa and Libya, backed by Russia and China, want the UN Security Council to suspend the ICC case against Mr Bashir but this is being resisted by other countries, led by the US and the UK.
On Monday, a group of mainly African relief and advocacy groups said the joint AU-UN force in Darfur - Unamid - was failing to protect civilians because it was too small and inadequately funded.
Only about a third of the intended 26,000 peacekeepers have been deployed.
"We are saying give peace a chance. Can you just give it a year, let's see Unamid deploying," Mr Kumalo said.
The UN estimates that five years of conflict in Darfur have left 300,000 people dead and more than 2 million people homeless.