BAGHDAD (AFP) - Pentagon chief James Mattis was in Baghdad on Tuesday (Aug 22) to show US support for Iraqi forces as they pressed an assault on Tal Afar, the Islamic State in Iraq and Syria (ISIS) group's last major bastion in the country's north.

Mr Mattis flew in for talks with Prime Minister Haider al-Abadi and other top officials, as well as Mr Massud Barzani, president of the Iraqi Kurdistan region, saying he wants to help keep the regime focused on eradicating ISIS militants.

"Right now our focus is on defeating ISIS inside Iraq, restoring Iraqi sovereignty and territorial integrity," Mr Mattis told journalists ahead of his trip to Baghdad.

Iraqi troops, supported by the forces of a US-led international coalition, routed ISIS in Mosul in July after a gruelling nine month fight for Iraq's second city.

On Sunday, they launched an assault on Tal Afar, once a key ISIS supply hub between Mosul - around 70km to the east - and the Syrian border.

In the desert plains around Tal Afar, convoys of tanks and armoured vehicles could be seen heading Monday for the militant-held city, raising huge clouds of dust.

Mr Mattis would not make any predictions on the fight.

"ISIS' days are certainly numbered, but it's not over yet and it's not going to be over anytime soon," said the US Defence Secretary.

Iraqi forces "fought like the dickens in Mosul, (it) cost them over 6,000 wounded, somewhere over 1,200 killed", he noted.

Yet that comeback restored the confidence of the Iraqi security forces after their shock loss of Mosul to ISIS in 2014.

Mr Mattis stressed that retaking Mosul would not have happened "without... Abadi's steady hand reconstituting that army, that was so shattered in 2014, an army he inherited".

But the comeback also leaned crucially on extensive training, planning and firepower support from the US military.

The future of that support must still be settled, and there will be resistance from Shiite militia and Iranians, said Mr Nicholas Heras, Middle East Security Fellow at the Centre for a New American Security in Washington.

KURDISTAN REFERENDUM CHALLENGE

Mr Mattis said discussions will focus on the way ahead, including how to keep Iraq from again politically fragmenting or falling further under Iran's influence, after four years united around battling the militants.

"Secretary Mattis is going to be very much focused on a pathway for the United States to continue to have a residual force in Iraq to continue to train Iraqi security forces" and avoiding a successor of ISIS from rising up, said Mr Heras.

A key issue is Iraqi Kurdistan's plan for an independence referendum on Sept 25, strongly opposed by the US as an event that could undermine Mr Abadi politically and distract from the fight against ISIS.

"A referendum at this time would be potentially catastrophic to the counter-ISIS campaign," said Mr Brett McGurk, the White House envoy to the anti-ISIS coalition.

"It's not just the United States; every member of our coalition believes that now is not the time to hold this referendum."

Mr McGurk said the initial push on the outskirts of Tal Afar was "going well", with 235 sq km cleared in the first 24 hours.

"That will be a very difficult battle," he said, but added that Iraqi and US forces are "moving faster, more effectively, more efficiently", in part due to US President Donald Trump having given Mr Mattis more authority to decide on tactics and resources needed.

Mr Mattis, who is on a five-day swing through Jordan, Iraq, Turkey and Ukraine, said he would also talk about reconstruction and the resettlement of hundreds of thousand of Iraqis driven from their homes and towns by the fighting, especially Mosul.

"It's not going to happen overnight. It's going to be a heavy lift for them going forward."

But Mr Heras said Mr Mattis, who he said has earned firm trust among Iraqis, needs to help Mr Abadi further build his power as a moderate for the post-war, with elections looming next year.

"That will be a political pickle that Mattis will have to work Abadi through," he said.

For Mr Mattis's meeting with Mr Barzani, Mr Heras added: "All signs point to it being one of those tough-love talks."