Iraqi government forces have made gains in their offensive to drive Islamic State militants from Falluja - one the country's two major cities in IS hands, BBC News said.

The nearby town of Karma, the first line of IS defence, is now in the army's hands, a BBC reports.

Large numbers of elite combat troops have also been deployed near Falluja, about 45km (28 miles) west of Baghdad.

But IS hit back north of Falluja, killing and injuring some Iraqi forces in a suicide car bomb attack.

A counter-attack south of the city was repelled with the help of helicopter gunships, the BBC reports.

This comes just days after the IS commander in Falluja, Maher al-Bilawi, was killed along with dozens of militants in U.S. -led coalition air strikes, according to Washington.