A spokesman said on the state TV channel that the operation had been named "Labeyk Ya Hussein".
The Baghdad-Kirkuk Highway has reopened. It had been closed since early March due to ISIL threats.
A police major said they had retaken the town of Husaiba al-Sharqiya, about 10 km east of Ramadi
Iraqi forces have said that they have fought off an attack near Ramadi which was taken by opposition forces over the weekend.
Allegedly, Saddam's ISIL commander nephew killed fighting for ISIL in Baiji.
With the fall of Ramadi to ISIL, Iraq's Prime Minister Haider al-Abadi has suffered a huge setback, and sent Shi'ite militiamen to reverse the capture
chairman of the U.S. military's Joint Chiefs of Staff, said in a statement that setbacks were "regrettable but not uncommon in warfare.
Funds to help them were running out and aid stocks were almost gone, the U.N. Office for the Coordination of Humanitarian Affairs in Iraq said.
The shiite militia had been ordered by Iraq to be deployed to Anbar with ISIL now advancing towards the group
Around 500 people were killed also between 6,000 and 8,000 people were displaced, a spokesman for governor of Anbar province told on Monday.
After the fall of Ramadi, Baghdad has ordered shiite paramilitaries to be deployed to Anbar.
ISIL said its members had taken full control over the Iraqi city of Ramadi on Sunday after overrunning a military base on the edge of the western provincial capital.
The Pentagon has said that if Ramadi falls, the US vows that it will help Baghdad to get it back.
The casualties occurred when armed group carried out suicide attacks on buildings of an operations command center and a military headquarters in the area.
ISIL in Iraq has taken control of government headquarters in the city of Ramadi
Iraq defence ministry says second in command of ISIL killed
At least seven people have been killed in separate explosions that have hit Baghdad today.
A prison break on Friday started when an inmate took a weapon from a warden at the prison on the main police compound in Khalis, a town around 50 kilometres north of Baghdad.
The Foreign and Trade minister for Hungary has said that they will join international efforts against ISIL
The Iraqi army and al-Hashid al-Shaabi forces lost 10 personnel while attempting to repel ISIL attack in Saladin.
Two rockets were fired into the heavily fortified zone, which is home to the prime ministers office and also houses Western embassies.