Troops had captured Timbuktu's airport and were set to take the entire storied city itself, al-Jazeera reported.
There were no updated reports on casualties.
Officials said rebels burned down City Hall, the governor's office and two buildings where the ancient texts were kept, a research center and a warehouse.
Mayor Halle Ousmani Cisse said destruction of the texts, some of which dated to the 13th century, was a "devastating blow" to world heritage, Britain's Guardian reported Monday.
Elsewhere in the country, people living in the northern city of Gao, on the River Niger, celebrated after French-led forces recaptured the city that had been under jihadist control since March 31, 2012.
Residents shouted "Liberte!" and "Vive la France!" in the streets, The Guardian said.
The French suffered no losses in the battle while about a dozen Islamic rebels were killed, the French Defense Ministry said.
Surviving rebels were reported to have fled on foot or by camel since there was no fuel for motor vehicles, The Guardian said.
Some Gao residents said they thought it was only a matter of time before the rebels would emerge again.
The books in the burned museum covered a wide range of topics, including astronomy, poetry, medicine and women's rights. Most were written in Arabic and some were in African languages, Hebrew and Turkish.
The texts were described as "priceless."
Seydo Traore a researcher, said the rebels also destroyed 300 shrines around the city dedicated to Sufi saints.