The Taleban have denied the reports, but have prevented anyone going to the museum to check on the artefacts.
Reports in Kabul say senior Taleban have destroyed more than a dozen ancient statues in the National Museum of Afghanistan.
The Taleban minister of information and culture has denied the reports but has refused to allow journalists to enter the museum to check them.
The museum lost most of its objects during the civil war.
But several pieces of world importance remained, including one Buddhist statue which experts say is priceless.
Fears
Reports started to circulate last week that the Taleban were destroyed non-Islamic artefacts in the museum, including statues of the Buddha dating back nearly 2,000 years.
The Taleban have denied the reports, but have prevented anyone going to the museum to check on the artefacts.
The head and deputy head of the museum were both out of the country last week when the alleged destruction occurred.
The museum has been closed to the public since the mid-1990s when most of the collection was looted by armed groups.
The on-going war has left only fragments and artefacts which were too heavy to steal.
These included Buddhist statues and bowls, ancient Hindu pieces, as well as Islamic relics - all precious evidence of Afghanistan's rich cultural past.
Now it seems even pieces from this tiny remnant of the collection have been destroyed.
Harsh brand of Islam
Islam wiped out Buddhism in Afghanistan 1,400 years ago.
But the presence of ancient Buddhist statues from the smallest miniature to the 50 metre-high Buddhist carved into a cliff face in the town of Bamiyan have posed problems for the Taleban.
With their ultra-conservative Islamic ideology, they believe a depiction of any human being is blasphemous.
They also think, mistakenly, that Buddhists worship the Buddha and that the statues are therefore idols.
The Taleban leader, Mullah Mohammed Omar, had ruled that the statues could be preserved so long as they were not worshipped.
But concern has persisted that a specially zealous Taleban could seek to destroy them.
There is particular worry now over one Buddhist statue, which was found in Kabul.
It is an exquisite one metre-high carving which is thought to be unique.
Experts say it is impossible to put a value on it.