Australia's Prime Minister Tony Abbott says he hopes legal hurdles can be cleared quickly so that Australian special forces troops can begin their assistance role in Iraq.

Australian jet fighters have flown their first missions over Iraq since Cabinet ministers approved their combat deployment on Friday.

The Cabinet also approved the deployment of a 200-strong ground force, including special forces, to "advise and assist Iraqi security forces" inside Iraq, subject to the Iraqi government providing legal guarantees.

Abbott said on Tuesday we would not give a time frame on when those guarantees might be provided.