The offer comes after a farcical opening to the new parliament, despite international leaders urging Iraq's fractious politicians to unite to help combat insurgents, as the military struggles to seize the initiative on the ground.
International leaders have warned Iraq's politicians there was no time to waste, while the head of a powerful jihadist group that led the militant advance urged skilled professionals to flock to help its newly proclaimed pan-Islamic state.
"I announce the provision of amnesty for all tribes and all people who were involved in actions against the state" but who now "return to their senses", excluding those involved in killings, Maliki said.
It was not immediately clear how many people the amnesty could affect, but analysts have said some form of political reconciliation will be necessary to convince Sunni Arabs angry with the Shiite-led government to turn against their co-religionists and jihadists.
Maliki's announcement came a day after an eagerly awaited opening to the Council of Representatives descended into chaos and ended in disarray as lawmakers traded heckles and threats.
So many Sunni and Kurdish deputies stayed away after a break meant to soothe soaring tempers that the quorum was lost and a speaker could not be elected, as constitutionally required.
UN special envoy Nickolay Mladenov said Iraqi politicians "need to realise that it is no longer business as usual".
Under a de facto agreement, the premier is a Shiite Arab, the speaker Sunni Arab and the president a Kurd.
Presiding MP Mahdi Hafez said the legislature would reconvene on July 8 if leaders were able to agree on senior posts.
