Their walk-out left the 40-member cabinet nearly half vacant and had negative impact on the post-war reconstruction and national reconciliation efforts.
Sunnis Arabs favored under Saddam Hussein's regime represent about 20 percent of the country's population. They lost their preference when Iraq's majority Shiites held sway after the former ruler's ouster in 2003.
Their rivalries led to a flare-up of sectarian fighting which aimed to tip the country into an all-out civil war.
The United States has been asking Prime Minister Nuri al-Maliki's government to bring back the Sunnis so that a genuine national reconciliation could be achieved to shore up a security gain.
Since late last year, the Iraqi government has taken actions in an effort to soothe the Sunnis.
The parliament passed a government-proposed amnesty law in February, which would free tens of thousands of detainees.
Iraq also has adopted a legislation through which more members of Saddam Hussein' Baath party will have access to government jobs.
Still, Maliki has ordered a series of security operations against outlaw militia, notably those belonging to Sadr.
Despite the return of the IAF, rifts are emerging within the Sunnis themselves.
The leading party within the Sunni bloc, the Iraq Islamic Party(IIP), is expected to face strong challenges in the upcoming provincial elections in October from grassroots Sunnis who accuse it of doing little to improve their lives.
