Gunmen killed two soldiers and snatched three more west of Baghdad on Saturday in apparent revenge attacks as mourners buried anti-government protesters that troops shot dead a day earlier.

The unrest came as lawmakers opposed to Nuri al-Maliki adopted a measure that would bar him from holding office beyond next year, as tensions rose dramatically after weeks of angry rallies in mostly-Sunni areas against the Shiite premier's rule.

In Fallujah, a predominantly Sunni town 60 kilometres (35 miles) from Baghdad, police Colonel Mahmud Khalaf said gunmen attacked checkpoints in the east, west and north, killing two soldiers, wounding one and kidnapping three.

The trio were on leave and wearing civilian clothes at the time they were snatched, army Lieutenant General Ali Ghaidan Majeed told AFP.

"We are conducting a search operation for them now."

No organisation immediately claimed responsibility for the attacks, which came a day after Iraqi troops opened fire on demonstrators in Fallujah, killing eight.

But militant Sunni factions, including Al-Qaeda's front group, often attack security forces to push Iraq back towards the sectarian war that blighted it from 2005 to 2008.

While some Shiite clerics have given cross-sectarian support to the rallies, Maliki blamed protesters and insisted soldiers had been "attacked."

The attacks on soldiers came as mourners buried the seven protesters shot dead on Friday, while an eighth person died of his wounds on Saturday. Some 59 others were wounded, according to Assem Hamdani, a doctor at Fallujah hospital.

"It is not only tense in Fallujah -- it is tense everywhere," Deputy Prime Minister Saleh al-Mutlak, a Sunni and a Maliki opponent, told AFP.

"It is almost out of control. It is becoming very worrying... It is getting very dangerous."

Friday's rally had been moving within Fallujah but was blocked by soldiers, who then opened fire after protesters began throwing bottles of water at them.

The defence ministry promised an investigation and handed over security in the town to the police in an attempt to defuse tensions.

On Saturday, thousands attended the funeral of the people killed, carrying the coffins of the victims through the streets of the town. At least one coffin was draped in an Iraqi flag dating back to the rule of now-executed dictator Saddam Hussein.

A demonstration followed the burials during which protesters shouted: "Listen Maliki, we are free people" and "Take your lesson from Bashar," a reference to Syrian President Bashar al-Assad, whose country is in the grip of a bloody 22-month uprising.

"I will not be satisfied with compensation provided by the defence ministry," said Ali Khalaf al-Ani, whose son Omar was killed on Friday.

"I want my son alive -- that is my demand!"

Maliki called for restraint by security forces in a statement issued by his office, but also said soldiers had been attacked in the first place.

"This is what Al-Qaeda and terrorist groups are seeking to exploit," he said of the apparent sectarian tensions.

The premier also blamed "conspiracies" propagated by the intelligence agencies of neighbouring countries, as well as Saddam and Al-Qaeda supporters.

The Fallujah demonstration was one of several across Sunni-majority areas of Iraq that have raged in recent weeks, hardening opposition against Maliki amid a political crisis ahead of provincial elections due in April.

In Baghdad, parliament passed a motion that would bar Maliki from a third term, a move his allies quickly dismissed as unconstitutional.

Lawmakers from three major Sunni, Kurdish and Shiite blocs that are all members of Maliki's unity government voted to limit Iraq's president, prime minister, and parliament speaker to two terms, in a move targeting the premier.

Maliki's supporters in parliament insisted the move would be felled by the courts, pointing to a previous ruling by Iraq's highest judicial authority that only the cabinet can propose legislation, not parliament.