More tombs in the ancient city of Timbuktu were destroyed at the weekend. The city is a UNESCO World Heritage site.
"Not a single mausoleum will remain in Timbuktu, Allah doesn't like it," Ansar Dine leader Abou Dardar told AFP on Sunday. "We are in the process of smashing all the hidden mausoleums in the area."
The United Nations on Thursday approved the deployment of a military force to Mali, where there was a coup in March.
Groups with links to al Qaeda have occupied northern Mali since April. Since then, they have destroyed much of the region's religious heritage and imposed strict Islamic law.
Timbuktu was a centre of Islamic learning from the 13th - 17th centuries. Its shrines are revered by Sufi Muslims.
Tourist official Sane Chirfi said four mausoleums there were razed on Sunday.
Ansar Dine and another rebel group on Friday denounced the UN decision, which will not take effect before September next year.