"Today we have a vigilance brigade so that no one touches the mausolea of Araouane and Gasser-Cheick," said Tahel Ould Sidy, leader of the unit, referring to two tombs in the greater Timbuktu region,
"We are armed and there is the required number of people," he added.
"We are not going to allow people who know nothing about Islam to come and destroy our treasures. I studied in Mauritania and Saudi Arabia, no one tells us in the Koran that we should destroy tombs."
Members of Ansar Dine (Defenders of Faith), an al-Qaeda-linked armed group which has been in control of northern Mali for over three months, on Tuesday destroyed two tombs in the city's oldest and biggest mosque, Djingereyber.
Last week they similarly destroyed seven tombs of ancient Muslim saints as well as the sacred door of another 15th century mosque, all listed as endangered World Heritage sites by Unesco.
They have vowed to destroy all similar sites in the fabled city, which they say are "haram" or forbidden by Islam.
A resident of the town said one wall of the Djingareyber mud mosque, built in 1325 according to Unesco, had partly fallen during the destruction of the tombs.
"On Tuesday night the Islamists rapidly rebuilt a part of the grand mosque's wall which fell when they destroyed the two mausolea," he said.
Experts say that while moderate Sufi Muslims, the majority in Mali, see the mausolea as shrines, those who follow the radical Wahhabi tradition see them as idolatrous.
In their eyes "other veneration is a sort of heresy, a way of stepping away from the oneness of God," said French anthropologist Jean-Claude Penrad.
Ansar Dine, along with al-Qaeda in the Islamic Maghreb and another jihadist offshoot, have controlled vast swathes of northern Mali since a northern takeover by armed groups in the wake of a March 22 coup. – Sapa-AFP