An Afghan man convicted of murder was executed in public on Wednesday, the Taliban said, the first confirmation of such a sentence since their return to power.

Last month Taliban supreme leader Hibatullah Akhundzada ordered judges to fully enforce aspects of Islamic law that include public executions, stonings and floggings, and the amputation of limbs from thieves.

They have carried out several public floggings since then, but Wednesday's execution in Farah – capital of the western province of the same name – is the first the Taliban have acknowledged.

"The supreme court was instructed to implement this order of qisas in a public gathering of compatriots," Taliban spokesman Zabihullah Mujahid said in a statement, referring to the "eye for an eye" justice in Islamic law.

In a later tweet, Mujahid said the victim's father had carried out the sentence, shooting the condemned man three times with a Kalashnikov.

The statement named the executed man as Tajmir, son of Ghulam Sarwar, and said he was a resident of Anjil district in Herat province.

It said Tajmir had murdered a man, and stolen his motorcycle and cell phone.

"Later, this person was recognised by the heirs of the deceased," it said, adding he had admitted his guilt.

The statement included the names of dozens of court officials as well as other Taliban representatives as being present for the execution. (AFP)