The Taliban made a fresh appeal on December 17 for Afghanistan's seat at the United Nations after the ambassador of the former U.S.-backed government left his post.
The UN seat, and some other embassies abroad, are at the centre of a tug-of-war between exiled diplomats of the old government and Afghanistan's new Islamist rulers.
No country has yet recognised the Taliban regime.
Assistant UN spokesman Farhan Haq told AFP that Afghan ambassador Ghulam Isaczai "relinquished his position as of December 15", according to a letter they received December 16.
The Taliban's nominee for the position, Suhail Shaheen, said the seat should be now given to the new government of Afghanistan, adding it was a matter of credibility for the world body.
The current government in Afghanistan "has sovereignty" over the country, he said on Twitter.
Early this month, the UN General Assembly passed a resolution indefinitely delaying a decision over the rival claims.
But even a month after the Taliban takeover, Mr. Isaczai was still being received at UN headquarters, and in November openly criticised the country's new rulers at a Security Council meeting.
When they previously ruled Afghanistan, from 1996 to 2001, the Taliban had no UN representation and their rule was recognised by just three countries -- Saudi Arabia, the United Arab Emirates and Pakistan.
UN-nominee Shaheen served as deputy ambassador to Islamabad during that period, becoming the movement's exiled spokesman after they were toppled and a favourite of foreign media because of his fluent English.