Nouri al-Maliki, who leads a government dominated by Shia Muslims, gave warning of a long fight ahead as 75 people died in a series of attacks in Baghdad and Baquba on Wednesday.
In his weekly televised address, Maliki appealed for international action against al-Qaeda and its affiliates, the Islamic State in Iraq and the Levant (ISIL).
"It may take time," he said "but ... to keep silent means there would be sub-states creating problems for the security of the region and the world."
Maliki called for "a strong position against countries who give support" to armed groups and urged world powers to "drain the resources of terrorists."
ISIL fighters and their local allies in the western Anbar province hold all of the former anti-government bastion of Fallujah and parts of the provincial capital Ramadi, farther west.
Ban Ki-moon, the UN secretary-general, and other diplomats have urged Iraq's leaders to seek political reconciliation to end the ongoing violence and the crisis in Anbar.
However, Maliki has ruled out dialogue with the fighters as his forces have launched wide-ranging security operations.
Deadly car bombings
So far, Maliki's strategy has failed to rein in the sectarian violence. Nine car bombs hit civilian targets on Wednesday in majority-Shia Muslim or confessionally mixed neighbourhoods of Baghdad, killing 37 people.
One of them struck a packed market in the Shaab neighbourhood, while another exploded outside a restaurant on Sanaa Street, killing five peoples, an AFP journalist reported.
The windows of nearby shops were shattered, the restaurant's ceiling partially caved in and blood and mangled vehicle parts scattered across the street.
The Baghdad attack could have been much worse, with police saying they managed to arrest four would-be suicide bombers, all allegedly Arabs of foreign nationalities, with explosives-rigged vehicles that were eventually disabled by security forces and military engineers.
They did not provide more details about the thwarted attackers, who they said were arrested in four different Shia neighbourhoods of Baghdad.
Elsewhere, a suicide bombing at a funeral in Buhruz, in religiously mixed Diyala province north of Baghdad, killed 16 people and wounded 20, officials said.
The funeral was for a member of the Sahwa, the Sunni Arab tribal militia who sided with the US military against their co-religionists in al-Qaeda's Iraqi branch from 2006, helping turn the tide against the group.
They are often targeted by Sunni Muslim fighters who regard them as traitors.
In and around the main northern city of Mosul, 13 people were killed, nine of them soldiers, while seven employees of a brick factory were shot dead in Muqdadiyah, 80km north of Baghdad.
Counterattack in Anbar
Meanwhile, in Anbar security forces attacked a town near Fallujah that had been seized by ISIL fighters and commandos swept in to clear the area, senior military officials said on Wednesday.
The counterattack came a day after fighters blew up an explosives-laden fuel tanker at an army checkpoint, killing three soldiers, on a small bridge near Saqlawiya, just north of Fallujah.
Heavily armed fighters then stormed into the town and surrounded the main police station, forcing all the policemen to relinquish their weapons and leave.
The fighters also retook a police station in Malaab, a major district of Ramadi, just days after Iraqi security forces declared success in the area.
However, following Wednesday's air raids against them, the fighters fled, allowing Iraqi troops to enter Saqlawiyah, the senior military officials said.
Clashes had erupted periodically in Ramadi and on the outskirts of Fallujah from Tuesday evening into Wednesday, with two children killed and 13 civilians wounded, security and medical officials said.
Fighting initially broke out in the Ramadi area on December 30, when security forces cleared a year-old Sunni Arab protest camp.
The violence spread to Fallujah, and fighters moved in and seized the city and parts of Ramadi after security forces withdrew.
Al JazeeraAl Jazeera