A nine-member credentials committee will now rule on the dueling requests, UN spokesman Stephane Dujarric told AFP, but it is unclear whether the committee will meet before the end of the convocation on Monday.
UN Secretary-General Antonio Guterres received a letter from Taliban-appointed Amir Khan Muttaqi "requesting to participate" in the high-level debate, Dujarric said.
It was dated Monday 20 September -- the day before the session got underway -- and listed Muttaqi as "minister of foreign affairs," he added.
The letter did not specify whether Muttaqi wanted to travel to New York to speak or whether the Taliban would submit a recorded video message, as many leaders are doing this year due to Covid-19.
The letter also indicated that Ghulam Isaczai "no longer represents" Afghanistan at the United Nations.
He was the ambassador to the UN of the Afghan government ousted from power in August as US military troops exited the country, ending their 20-year war.
The letter said that the Taliban had nominated their Doha-based spokesman Suhail Shaheen as Afghanistan's permanent representative to the UN.
The note, which had the letterhead "Islamic Emirate of Afghanistan, Ministry of Foreign Affairs," said that former president Ashraf Ghani was "ousted" on 15 August, the day he fled the country.
"Countries across the world no longer recognise him as president," the letter said, according to the UN.
The UN spokesman also said that secretary-general Guterres had received a separate letter from Isaczai, dated 15 September, containing the list of Afghanistan's delegation for the session.
That letter listed Isaczai as Afghanistan's permanent representative, Dujarric said.
"These two communications have been sent by the secretariat, after consultation with the office of the president of the General Assembly, to the members of the credentials committee of the 76th session of the General Assembly," he said.
The committee is made up of Russia, China, the United States, Sweden, South Africa, Sierra Leone, Chile, Bhutan and the Bahamas.
The committee has in the past refrained from making a decision and instead referred it to the General Assembly for a vote, a diplomatic source told AFP.
No government has yet recognized the Taliban government, first demanding that it meet commitments on human rights, but some have made positive noises.
"The pragmatic, political view is that there is a new reality. And if you want to ignore that, that's your choice," Shah Mahmood Qureshi, foreign minister of the Taliban's historic backer Pakistan told reporters Monday, stopping short of calling for legal recognition.