Prime Minister Nuri al-Maliki's offer yesterday came after a farcical opening to the new parliament in Baghdad, despite international calls for Iraq's fractious politicians to unite urgently to combat insurgents, as the military struggles to seize the initiative against the Sunni militants.
With hopes of a unity government waning, Washington reached out to regional players with President Barack Obama calling Saudi Arabia's King Abdullah and Vice President Joe Biden contacting the speaker of Iraq's previous parliament, Osama al-Nujaifi, a prominent Sunni leader.
Secretary of State John Kerry meanwhile phoned Kurdish leader Massud Barzani and stressed the important role the Kurds would play in a new multi-sect government in Baghdad, seen as vital to meeting the challenge of Islamic State (IS) jihadists who have seized vast tracts of Iraqi territory, according to spokeswoman Jen Psaki.
Maliki's surprise move meanwhile appeared to be a bid to split the broad alliance of jihadists, loyalists of executed dictator Saddam Hussein and anti-government tribes waging the offensive.
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But he excluded those involved in killings, and it was not immediately clear how many people might be eligible.
Analysts have said some form of political reconciliation is needed to convince Sunni Arabs angry with the Shiite-led government to turn against their co-religionists and jihadists.
The vast majority of Iraq's Sunni Arab minority do not actively support the IS jihadist group spearheading the offensive, but analysts say anger over perceived mistreatment by the authorities means they are less likely to cooperate with the security forces.
UN special envoy Nickolay Mladenov said Iraqi politicians "need to realise that it is no longer business as usual."
Under a de facto agreement, Iraq's premier is a Shiite Arab, the speaker Sunni Arab and the president a Kurd.