“Not a single mausoleum will remain in Timbuktu,” Abou Dardar, a leader of the Islamist group Ansar Dine, told AFP news agency.
Islamists in control of northern Mali began earlier this year to pull down shrines that they consider idolatrous.
Tourist official Sane Chirfi said four mausoleums had been razed on Sunday.
One resident told AFP that the Islamists were destroying the shrines with pickaxes.
Timbuktu was a centre of Islamic learning from the 13th to the 17th centuries.
It is a UN World Heritage site with centuries-old shrines to Islamic saints that are revered by Sufi Muslims.
The Salafists of Ansar Dine condemn the veneration of saints.
“Allah doesn’t like it,” said Abou Dardar.
“We are in the process of smashing all the hidden mausoleums in the area.”
Islamists seized control of Timbuktu in April, after a coup left Mali’s army in disarray.
The news that further monuments were being destroyed came one day after Islamists were reported to have cut the hands off two people.
The Movement for Oneness and Jihad in West Africa, another Islamist group operating in the area, warned that there would be further amputations, AFP reported.
Last Thursday the UN Security Council gave its backing for an African-led military operation to help Mali’s government retake the north if no peaceful solution can be found in coming months.
A day later, Ansar Dine and the Azawad National Liberation Movement (MNLA), a Tuareg separatist group, said they were committed to finding a negotiated solution.
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