If the peshmerga succeed in recapturing the town, it would open up a corridor to Sinjar mountain, where hundreds of minority Yazidis have been besieged by militants since August.
"At 8:00 this morning the ground offensive began to liberate Sinjar town," said one official in the region's Security Council, adding that coalition planes had pounded the area for several hours beforehand.
Kurdish peshmerga forces took control of two villages from the ISIL, according to another peshmerga source.
The villages are near Mosul in the Erbil province of northern Iraq,
“The peshmerga forces started their attack at 4 a.m. local time (0100GMT) after airstrikes by the U.S-led international coalition,” Rashid Haji Ali, a Peshmerga commander, told The Anadolu Agency.
ISIL militants were forced to retreat from the two villages, because of intensive coalition airstrikes and the peshmerga’s ground offensive operation, the commander said.
“We are attempting to control all the area around Sinjar mountain,” Ali added.
ISIL controls most of the Sinjar, which is 77 miles west of Mosul.