Parts of the massive statues - the larger of the two was believed to be the world's tallest standing Buddha - have been destroyed and demolition will continue when Eid ends Thursday, Abdul Salam Zaeef, the Taliban's ambassador to neighboring Pakistan, said in Islamabad.
``We don't know how long it will take to destroy them, but they will be eliminated,'' he said.
The Taliban's reclusive leader Mullah Mohammed Omar has ordered all pre-Islamic statues in the country destroyed, including the two towering Buddhas hewn from a cliff face in central Bamiyan in the third and fifth centuries.
Their destruction, as well as thousands that of other relics, including a 2,000-year-old seated bodhisattva Buddha, has generated international outrage. In Buddhism, bodhisattvas are people of great spiritual awareness who help others reach enlightenment.
An eyewitness report earlier said Taliban soldiers were firing anti-aircraft weapons at the giant statues.
``I am being told from Kabul that they are using mainly explosives because the statues are very strong,'' Zaeef said. ``We do not want to spend more money or resources to destroy them. That's why we are using explosives.''
Reporters trying to reach Bamiyan, a valley in the Hindu Kush Mountain range nearly 80 miles from the Afghan capital of Kabul, were turned back by Taliban troops armed with automatic weapons.
Most other Buddhist statues in museums throughout Afghanistan have already been destroyed, said Taliban officials who did not want to be quoted.
It's not known whether the priceless bodhisattva is among them, but one Afghan source said ``everyone believes it has been demolished. No one believes it is still there.''
Islamic clerics within the Taliban ranks were outraged by the bodhisattva's naked torso when the Kabul Museum was briefly opened last August. The statue was quickly encased in glass.
``It is one of the most beautiful, ethereal Buddha statues. It was in superb condition,'' Carla Grissman, who spent several years in Afghanistan compiling an inventory of the Kabul Museum collection, said in a telephone interview from Britain where she now lives.