An American navy veteran detained in Afghanistan for more than two years was released by the Taliban on Monday in exchange for a key ally, Afghanistan's foreign minister said.

Mark Frerichs was working as a civil engineer on construction projects in Afghanistan when he was "taken hostage" in 2020, the United States has previously said.

"After long negotiations, US citizen Mark Frerichs was handed over to an American delegation and that delegation handed over (Bashar Noorzai) to us today at Kabul airport," Foreign Minister Amir Khan Muttaqi said at an event held in the capital to announce the exchange.

The Taliban seized power in Afghanistan a little over a year ago as the United States and their NATO allies withdrew from the country after 20 years of military intervention.

No country has yet to recognise the new government, with Washington repeatedly telling the Taliban that they will have to "earn" legitimacy.

The US state department had previously described the veteran's release as one of the government's "core, non-negotiable priorities".

"The Taliban must immediately release Mark before it can expect any consideration of its aspirations for legitimacy. This is not negotiable," US President Joe Biden said in a statement in January.

Noorzai, a warlord and Taliban associate, was sentenced to life imprisonment for heroin smuggling and had served 17 years in a US jail.

While he held no official position, he had "provided strong support including weapons" for the Taliban in the 1990s, government spokesman Zabihullah Mujahid told AFP.

His return to Kabul was celebrated with a hero's fanfare by the government of the new Islamic Emirate of Afghanistan (IEA), the name the Taliban have given the nation since seizing power last August.

Photographs show he was greeted by masked Taliban fighters bearing floral garlands.

"If the IEA had not shown its strong determination, I would not have been here today," Noorzai told reporters at the event in Kabul.