Australian special forces are ready to start work in Iraq as soon as final paperwork is sorted out.

Prime Minister Tony Abbott says Australia is finalising the legal documentation that gives authority for special forces soldiers to help support and train Iraqi troops as part of the fight against Islamic State.

“We’ve written to the Iraqis, the Iraqis have written back to us and we now need to consider their response to finalise our considerations,” he told reporters in Canberra on Tuesday.

“I hope that can be done very quickly because it is an absolutely critical mission upon which our forces will be embarked.”

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Australia started flying combat missions over Iraq on Sunday as part of the international coalition combating the IS terrorist group.

In that first operation, two RAAF Super Hornets conducted an armed patrol over Iraq but they did not attack any targets.

It’s expected the crews will fly more combat missions in the coming week.