BAGHDAD - An alliance spearheaded by prominent Shiite cleric Moqtada al-Sadr looked on course on Monday for a surprise triumph at Iraq's first nationwide election since the defeat of the Islamic State terror group last year.

In a further political upset, the Conquest Alliance of former fighters appeared to be coming in second, squeezing incumbent Prime Minister Haider al-Abadi into third.

The outcome throws open the race to become the next prime minister, as millions of Iraqis went to 8,959 polling centers across the country on Saturday to vote for their parliamentary representatives in the first general election after Iraq's victory over the IS group in December.

Some 90 political entities and 7,000 candidates were vying for 329 seats in the parliament.

Sadr himself did not run for parliament and so cannot be a candidate for the prime minister's post. But a significant number of seats for his movement would give him a strong voice in building the next government.

With 16 of 18 provinces counted, Sadr's Marching Towards Reform alliance was ahead in six and second in four regions.

"We are moving to a free and independent Iraq," Sadr said just before Saturday's voting in a televised address from his office in the Shiite city of Najaf.

"We are going to move to an Iraq safe from corruption, terrorism and militias," he said.

He warned that if there were manipulation and fraud in the election, "we will make the earth quake beneath the feet of the cheaters and corrupt".

Next in the running was the Conquest Alliance, made up of ex-fighters from paramilitary units that battled the IS, with results putting them ahead in four provinces and second in eight others.

The complex electoral arithmetic of the Iraqi system, however, means that the final makeup of 329-seat parliament is still far from decided.

In a televised address on Monday afternoon, Abadi hailed the "winning lists" and called on all sides to "respect the results", after calls for a recount in the multiethnic province of Kirkuk.