Adnan Pachachi, the acting speaker, opened the only second session of the parliament since it was elected in December.
Hopes of ending four months of political deadlock have been raised after Shia politicians agreed to nominate al-Maliki in place of the incumbent, Ibrahim al-Jaafari.
The nomination of the tough-talking Shia leader has won initial approval from senior Sunni and Kurdish representatives - support the Shia alliance needs if it is to build a unity government.
At a press conference on Friday, al-Maliki sought to outline how his administration would govern a country plagued by sectarian conflict and instability.
"We are going to form a family that will not be based on sectarian or ethnic backgrounds," he said.
"I intend to form a national unity government that will face the challenges of terrorism and corruption."
"Each ministry will be run professionally and not as minister's own property, dictated by his ethnic background."
Sunni and Kurdish politicians had blamed al-Jaafari for the rise in sectarian tensions in Iraq and for failing to rein in Shia militias working alongside the Interior Ministry.
If confirmed, al-Maliki will have a month to form a cabinet with officials overseeing powerful ministries, including the interior, defence and oil portfolios, which could also require difficult negotiations.
Al-Maliki is a close ally of al-Jaafari and has a reputation as hardline member of the Dawa party, the oldest Islamist party in Iraq.