A militant posing as a construction worker killed a Sunni Iraqi MP and six others on Tuesday by wrapping his arms around the lawmaker before blowing himself up, as a political row engulfs Iraq.

The killing of Ayfan Saadun al-Essawi comes just two days after Finance Minister Rafa al-Essawi, a fellow Sunni and a member of the same tribe and political bloc, escaped an apparent assassination attempt as his convoy passed near where Tuesday's attack took place.

No group immediately claimed responsibility, but Sunni militants often target officials and high-profile individuals in a bid to destabilise the government and push the country back towards the bloodshed that raged from 2005 to 2008.

Essawi's killing is likely to further enflame tensions, with Iraq already grappling with a political crisis pitting Prime Minister Nuri al-Maliki against Essawi's secular Sunni-backed Iraqiya bloc.

Essawi, 37, had been inspecting a road being paved south of Fallujah when the attacker, who was dressed as a construction worker, came up to him.

"The moment he stepped out of the car to check out this road between Fallujah and Amriyah, at this moment, there was a man," said Sohaib Haqi, the lawmaker's office chief. "He came to him, hugged him, said Allahu Akbar (God is greatest), and blew himself up."

Fallujah hospital's Doctor Assem al-Hamdani put the overall death toll at seven dead -- Essawi, four of his bodyguards and two civilians. Another six were wounded, including four of the lawmaker's guards.

Three days of mourning were declared in Anbar province, and the lawmaker's funeral was expected to be held on Wednesday.

Essawi was also a former leader of the Sahwa, a collection of Sunni tribal militias that turned against Al-Qaeda and sided with the US military from late 2006, helping turn the tide of Iraq's bloody insurgency.

He was himself inducted into parliament after another Sunni MP, Khaled al-Fahdawi, was killed in a suicide attack at Baghda's Umm al-Qura mosque in 2011.

One MP voiced fears the killing could further raise tensions.

"It aggravates the political conflict," independent Kurdish MP Mahmud Othman told AFP. "I hope these crimes and incidents will urge political leaders to meet and try to find a solution, because there is no other way."

Weeks of anti-government demonstrations in Sunni Arab majority areas, supported by Iraqiya and other groups, have hardened opposition against Maliki, a Shiite.

The premier is at loggerheads with Iraqiya, which remains a part of his national unity government, over its accusations of Maliki acting in an authoritarian and sectarian fashion in the run-up to key provincial polls.

Kurdish parties and powerful Shiite cleric Moqtada al-Sadr, whose movement counts 40 members of parliament and five ministers among its ranks, have also publicly opposed Maliki.

The demonstrations in Sunni areas have decried alleged misuse of anti-terror laws to detain members of the minority community, and claim Sunnis are being targeted by the Shiite-led authorities.

In a bid to placate the demonstrators, a top minister publicly apologised on Monday for holding detainees for prolonged period without charge and said Baghdad had released 335 prisoners in the past week.

The crisis comes with barely three months to go before provincial elections, a key barometer of support for Maliki and his opponents ahead of a general election next year.