Al-Abadi called for the additional support after a meeting late Saturday with delegates from the Anbar Provincial Council.
Iraq’s prime minister said his country and Turkey have agreed on closer security and intelligence cooperation.
Kurdish forces, backed by US-led airstrikes, launched a new offensive Wednesday targeting the Islamic State group.
No group immediately claimed responsibility for the midday attack near the ancient citadel in Irbil.
A US-led coalition is carrying out air strikes against IS jihadists in both Iraq and Syria.
Car bomb blasts in two northern Baghdad neighbourhoods killed at least 17 people and wounded at least 57.
The officials say that Iraqi troops on Friday also lifted the Islamic State group’s siege of the oil refinery, Iraq’s largest.
A suicide bomber rammed his explosives-laden car into a military outpost, killing seven soldiers.
The airstrikes on Friday night destroyed a convoy consisting of 10 Islamic state armed trucks, said an official.
Top Interpol officials said that would-be jihadi fighters are booking tickets on cruise ships to join extremists.
Britain is sending more troops to train Iraqi and Kurdish fighters battling Islamic State militants.
New Zealand says it won’t send combat troops to Iraq to directly fight the Islamic State group.
Huge crowds of Shiites gathered in Iraq and Lebanon on Tuesday to mark a key holy day in defiance of jihadists.
Bombings in the Baghdad area killed at least 24 people on Saturday, just days ahead of Shiite commemorations.
The UN Security Council is expressing its “deep outrage” at the killings, rapes and torture by the Islamic State.