Peacekeeping chief Alain Le Roy said the UN spent three hours trying to persuade the government to let the airlift take place.
Three wounded soldiers died while the negotiations were being held, he said.
The peacekeepers were sent earlier this month to Abyei, claimed by Sudan and the newly independent South Sudan.
Within days of their arrival from Ethiopia, their convoy hit a landmine in Mabok, south-east of Abyei town.
One peacekeeper died instantly while another three died later, said Mr Le Roy, the UN Undersecretary General for Peacekeeping.
"We didn't get the clearance for the Medivac helicopter to take off immediately," he said.
"They prevented us from taking off by threatening to shoot at the helicopter."
Mr Le Roy said "no-one can say" whether the delay in airlifting the peacekeepers had contributed to their deaths.
But he said the crew of the Medevac helicopter complied with the delay because Sudanese troops threatened to shoot them down if they took off without clearance.
Le Roi said there is no way to know whether the three peacekeepers, critically injured in a land mine blast, would have survived if they had been moved sooner.
A U.N. spokesperson said Secretary General Ban Ki-moon had taken the issue to Sudan's ambassador to the U.N. The spokesperson said Mr. Ban stressed that any delay is “unacceptable” when it comes to saving lives.
The three peacekeepers were wounded Tuesday in a blast while on patrol in the disputed Abyei region. A fourth peacekeeper died instantly in the explosion. Seven others were wounded but survived.
Ethiopia provided the troops for the recently-approved Abyei peacekeeping force.
Abyei sits on the border between Sudan and the new nation of South Sudan. The two countries have been unable to decide which one should control the oil-rich region.
Sudanese troops occupied Abyei on May 21, about seven weeks before South Sudan declared independence.
Both sides have agreed to withdraw their forces under a deal that led to the creation of the U.N. peacekeeping force.