Iraq plans to hold parliamentary elections on May 15 to choose a prime minister, a statement from the prime minister's office said late on Tuesday.

Prime Minister Haider al-Abadi hasn't yet said if he plans to seek a new term. Most executive power is held by the prime minister, who is also commander of the armed forces.

The May 15 date, agreed at a government meeting on Tuesday, has yet to be approved by parliament.

Abadi took over the premiership in 2014 from Nuri al-Maliki, a close ally of Iran held responsible for the army's collapse as Islamic State (IS) militants swept through a third of Iraq.

Abadi is credited for quickly rebuilding the army and defeating IS in its main Iraqi stronghold, Mosul, last July, with strong assistance from a U.S.-led coalition.

Maliki holds the ceremonial title of vice-president. As head of the Shia Dawa party and the largest block in parliament, he remains a powerful political figure.

The prime minister's office is reserved for Iraq's majority Shia Arab community under a power-sharing system set up after the 2003 U.S-led invasion that toppled Saddam Hussein, a Sunni Arab.

The largely ceremonial office of president is reserved for a Kurdish member of parliament. The speaker of parliament is drawn from Sunni Arab MPs.