The Iranian-born grand ayatollah Ali al Sistani also wants them to agree on the next parliament speaker and the president before the legislature's inaugural session.
A cleric representing Mr Sistani told worshippers in the holy city of Karbala selecting the three before parliament meets would be a "prelude to the political solution that everyone seeks at the present".
The urgency reflects the deep crisis in Iraq after Sunni militants blitzed through the north and west this month, capturing vast areas of territory, including the second-largest city, Mosul.
Iraq's political leaders have been under growing pressure from the West and elsewhere to form an inclusive government.
The call - issued by a cleric representing Mr Sistani, Abdul-Mahdi al Karbalaie - steps up pressure on political leaders to set aside their differences and form an inclusive government in the face of sweeping gains by the Islamic State of Iraq and the Levant and allied militants.
Iraq's political leaders are being pressed by the US, Baghdad's main Western backer, which hopes such a government would diminish support for the militants among the disaffected Sunni minority.
The reclusive Mr al-Sistani is the most revered figure among Iraq's Shi'ites.
A call up to arms he issued on June 13 prompted tens of thousands to volunteer to join the security forces in the fight against the extremists, with truckloads of volunteers gathering in Baghdad before being transported north to fight the militants.
However, asking the political blocs to agree on the nation's three top jobs in four days could prove to be a tall order even at this time of crisis.
Iraq's Shi'ite, Sunni and Kurdish leaders have been bickering among themselves for years and it took them nine months to form a government after parliamentary elections in 2010.