“The number of people displaced by the conflict continues to increase and is approaching 195,000, including nearly 100,000 who have fled abroad,” read a statement from the agency.
The refugees have headed mostly to Mauritania, Niger, Burkina Faso and Algeria.
Tuareg rebels are waging their biggest offensive since a 2009 rebellion as they demand autonomy in Mali’s vast north, and have launched several attacks on towns in the region since mid-January.
There have been reports of scores of executions, and deaths of civilians and soldiers in the fighting.
Many of the refugees are fleeing to areas facing severe food shortages as a result of low rainfalls, meagre harvests and high food prices.
A nomadic community of some 1.5 million people, Tuareg of various tribes are scattered between Algeria, Burkina Faso, Libya, Niger and Mali.
Mali and Niger experienced uprisings as the Tuareg fought for recognition of their identity and an independent state in the 1960s, 1990s and early 2000s, with a resurgence between 2006 and 2009.
Many Tuareg left for Libya where they later fought for Moamer Kadhafi’s regime, but after his death in October they returned home, some heavily armed.