Australia backs the United States-led airstrikes on Islamic State strongholds in Syria but appears unlikely to participate.
The US and its Arab allies have unleashed deadly bomb and missile strikes on jihadists in the IS-held city of Raqa and near the border with Iraq, opening a new front in the conflict.
While Prime Minister Tony Abbott has previously refused to rule out contributing to a military campaign in Syria, Ms Bishop has made it clear that, for now at least, Australia's focus remains on Iraq.
"We have been asked to focus our efforts on Iraq, we are working closely with the Iraqi government," Ms Bishop told reporters on Tuesday after counter-terrorism talks in New York.
Australia has not been asked to participate in Syria, she said.
About 600 Australian Defence Force personnel have pre-deployed to the United Arab Emirates ahead of a likely engagement in Iraq in the coming weeks.
Ms Bishop, who intends to travel to Iraq within days, says Australia's military role there will be "prudent and proportional".
Ms Bishop made it clear Australia supports the Syrian strikes, despite being launched without Syrian or United Nations approval.
"The foreign ministers that I have spoken to from the region support it," she said.
"They see this ungoverned space in eastern Syria is a breeding ground for this type of terrorism."
Bahrain, Jordan, Saudi Arabia, Qatar and the United Arab Emirates joined the operation.
Dozens of IS and al-Qaeda militants were reported to have been killed in the raids.
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