Iraqi party leaders planned delicate talks over the weekend that could end Prime Minister Nouri al-Maliki's divisive rule, after a top Shi'ite cleric Friday called for a new premier to be chosen without delay to tackle Islamist rebels threatening to tear apart the country.

Major foreign powers are pushing for a new inclusive government, rather than one pursuing Shi'ite sectarian domination, to be formed fast to counter the insurrection that has spilled across the border with Syria and could menace the wider Middle East.

In a striking political intervention on Friday that could signal the demise of al-Maliki's eight-year tenure, influential Grand Ayatollah Ali Sistani urged political blocs to agree on the next premier, parliament speaker and president before a newly elected legislature meets in Baghdad on Tuesday.

"The next 72 hours are very important to come up with an agreement to push the political process forward," said a lawmaker and ex-government official from the National Alliance, which groups all Shiite Muslim political parties.

The lawmaker, who asked for anonymity because of political sensitivities, said he expected internal meetings of the various parties and a broader session of the National Alliance including al-Maliki's State of Law list to be held through the weekend. Some Sunni Muslim parties were to convene later on Saturday.

Sistani's entry into the fray will make it hard for al-Maliki to stay on as caretaker leader as he has since a parliamentary election in April. That means he must either build a coalition to confirm himself in power for a third term or step aside.

Sistani's message was delivered after a meeting of Shiite factions including the State of Law coalition failed to agree on a consensus candidate for prime minister.

The embattled al-Maliki accused his political foes of trying to prevent parliament from meeting on time and whipping up violence to interfere with the political process.

"They worked to postpone the elections ... and now they are working to postpone the first session of the council of representatives ... but if they are not able to pressure us to postpone, they will go for inciting security incidents in Baghdad," he said during a televised meeting with commanders.

Since early June, the Sunni terrorist army of the Islamic State in Iraq and Syria has overrun most majority Sunni Muslim areas in the north and west of Iraq, capturing the biggest northern city Mosul and late dictator Saddam Hussein's hometown of Tikrit.

ISIS aims to set up a medieval-style Islamic caliphate erasing regional borders, and they deem all Shiites to be heretics deserving death. They have boasted of executing scores of Shiite government soldiers captured in Tikrit.

On Saturday, Iraqi troops were trying to advance on Tikrit from the direction of Samarra to the south that has become the military's line in the sand against an ISIS charge southwards to within an hour's drive of the capital Baghdad.

U.S. President Barack Obama has ruled out sending ground forces back to Iraq, where they were for eight years after invading to oust Saddam, but has sent up to 300 advisers, mostly special forces, to help the government take on ISIS.

U.S. defense officials said on Friday that the Obama administration was flying armed aircraft over Iraq although these aimed to collect intelligence and ensure the safety of U.S. personnel on the ground rather than attack targets.

Gen. Martin Dempsey, the top U.S. military officer, said additional U.S. options included going after "high value individuals who are the leadership" of ISIS and working to protect Iraq's "critical infrastructure".

On Saturday, 11 people were injured when an explosion rocked a health ministry building in insurgent-held Mosul, a local health official said. City residents said the blast was caused by a drone strike, but a U.S. official dismissed this possibility.

Residents also reported overnight rocket fire into the city of Mosul, which fall to ISIS on June 10 allowing the militants to sweep across the north where they also took border crossings with areas of civil war-racked Syria that they already controlled.

Under Iraq's governing system put in place after Saddam's overthrow, the prime minister has always been a Shiite, the largely ceremonial president a Kurd and the speaker of parliament a Sunni. Negotiations over the positions have often been drawn out. After the last election in 2010 it took nearly 10 months for Maliki to build a coalition to stay in office.

Divvying up the three posts in the four days before parliament meets, as sought by Sistani, would require leaders from each of Iraq's three main ethnic and sectarian groups to commit to the political process and swiftly resolve their most pressing political problems, above all the fate of Maliki.

Maliki, whose State of Law coalition won the most seats in the April election, was positioning himself for a third term before the ISIS offensive began. His closest allies say he still aims to stay, but senior State of Law figures have said he could be replaced with a less polarising figure.

"It's a card game and State of Law plays a poker game very well," said the official from the premier's alliance. "For the prime minister, it will go down to the wire."