FALLUJAH, Iraq (AFP) - 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 theoretically bar him from holding office beyond next year, as tensions rose dramatically after weeks of angry rallies in mostly-Sunni areas against the premier's rule.

In Fallujah, a predominantly Sunni town 60 kilometres from Baghdad, police Colonel Mahmud Khalaf said gunmen attacked checkpoints in the east, west and north of the town on Saturday, killing two, 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 incidents, which came a day after seven demonstrators were shot dead in Fallujah, 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 Shia clerics have given cross-sectarian support to the rallies, Maliki blamed protesters and insisted soldiers had been "attacked."

The attacks on soldiers came as funeral-goers buried the protesters shot dead a day earlier.

Friday's rally had been moving within Fallujah but was blocked by soldiers, police Captain Nasser Awad said.

Protesters began throwing bottles of water at the troops, who opened fire. Seven demonstrators were killed, all of them from gunshot wounds, said Assem al-Hamdani, a doctor at Fallujah hospital.

Hamdani said 60 others were wounded, most by gunfire.

The defence ministry promised an investigation, and security responsibilities in the town were transferred to the police in an attempt to defuse tensions.

On Saturday, thousands attended the funeral of the people killed.

A demonstration followed the burials during which protesters shouted: "Listen Maliki, we are free people" and "Take your lesson from Bashar," a reference to embattled 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, referring to an offer for financial compensation by Baghdad.

"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, supporters of now-executed Iraqi dictator Saddam Hussein and Al-Qaeda.

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 the Sunni-backed Iraqiya bloc, the main Kurdish alliance and the movement loyal to powerful Shia cleric Moqtada al-Sadr - all of which have ministers in Maliki's national unity government - backed the move to limit Iraq's president, prime minister, and speaker of parliament to two terms.

The move appeared to target Maliki, as the other two posts are held by members of Iraqiya and the Kurdish bloc.

The prime minister's supporters in the Council of Representatives 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.