Prime Minister Malcolm Turnbull says Australia doesn't want to be in Iraq forever and the most important boots on the ground in the fight against Daesh have to be Iraqi.
Addressing Australian and New Zealand troops at Taji where they're training Iraqi soldiers, he said this had to be an Iraqi victory, although the coalition would contribute, including through training, advice and air power.
The prime minister said the Australians and New Zealanders were making a vital difference in rebuilding and training the Iraqi army that would destroy Daesh.
He said the current international program to train the Iraqi army was committed to training up 10 army brigades and it would then come to an end.
Any further commitment would depend on the circumstances, he said.
"We do not intend to be in Iraq forever. It has been a long time," he said.
"In terms of visible boots on the ground it has to be seen by the Iraqi people, it has to be seen to be them regaining control of their own country." Mr Turnbull flew from the United Arab Emirates into Iraq on Saturday, first landing in Baghdad where he held talks with Iraqi Prime Minister Haider al-Abadi.
Speaking at the post-meeting media conference in Baghdad, he told the prime minister he filled us with confidence that victory against Daesh in Iraq was within reach.
"That is encouraging, but the victory must be one that endures. And for it to endure there must be genuine reconciliation between the various parties in Iraq," he said.
At each stop he thanked Australian troops for their contribution to the fight against Daesh.
"You are here to rebuild and train the Iraqi army that will destroy Daesh," he said in Taji, a sprawling military base a short distance north of Baghdad.
"Australians, New Zealanders are making a vital difference in defeating Daesh. That will be so important not just for Iraq but for the whole world." Mr Turnbull said their work was having a global impact, making the world safer.
Australia is the second-largest contributor to the coalition in Iraq, after the United States.
Three hundred Australians are training the Iraqi military, alongside 100 New Zealanders. Another 80 Australian special forces are advising Iraqi special forces while the air task group conducts missions over Iraq and Syria.
Mr Turnbull affirmed that Australia would not be increasing the already substantial contribution to the conflict in Iraq and Syria. That followed a request from the US directed at Australia and some 40 other nations.
"We are encouraging other countries, particularly other European countries, NATO countries to step up," he said.
The US-led coalition's efforts appear to be paying off with ISIL-held territory shrinking by about 40 per cent from its maximum expansion in Iraq in 2015.
On Tuesday (US time), Mr Turnbull will visit the White House on his first trip to the US since assuming office in September 2015.
Mr Turnbull and President Barack Obama will discuss Iraq and Syria as well as trade issues.
