Vast territory in Syria's north-east is "ungoverned space", Foreign Minister Julie Bishop has suggested, following talks in New York, as questions continued about the legal basis for US attacks launched on Tuesday on key Islamic State targets in the country.

This latest description suggested the government of Syria was no longer sovereign in its previous territory and a signal that sufficient legal grounds could be found to allow the US to undertake bombing missions on targets deep inside that country.

Ms Bishop's comments came after meetings with international leaders and officials on the challenge posed by IS, also known as ISIL, and she also revealed that she had been invited to Iraq by that country's foreign minister and hoped to take up that invitation in coming weeks.

The US and some Arab state partners attacked key IS targets on Tuesday using aerial bombing and missiles launched from the sea.

International law experts have previously queried the basis of military intervention in Syria in the absence of either a dedicated UN resolution or a specific invitation to enter the territory from Damascus.

Syria, unlike Iraq, has not invited the US and allied western forces into its territory to help defeat IS, and the brutal dictatorship of Bashar al-Assad is strongly opposed by the west and most other nations.

Prime Minister Tony Abbott has previously stated that Australia does not recognise the government of Syria - which has launched murderous attacks on its own people.

However, support from Russia and potentially from China means a resolution seeking clear legal authority to enter Syrian territory is unlikely.

Ms Bishop also cited the legal concept of "collective self-defence" to allow the US to take necessary action to pursue IS into Syria if it was being used as a staging ground for attacks on US citizens and national interests.

However, she denied that this could be used by Australia to also conduct missions in Syria, stating that while Australia's role in the mission was yet to be finalised, it would be limited to supporting the fight against IS in Iraq rather than in Syria.

Mr Abbott arrives in New York on Wednesday for two days of meetings with world leaders on the crisis engulfing Iraq and Syria. His schedule includes a meeting of the powerful UN Security Council, on which Australia is a temporary elected member, to be chaired by US President Barack Obama.

Ms Bishop said she expected the meeting to be a broad-ranging discussion by many countries about the global terrorist threat, but the specific resolution would deal with the problem of foreign fighters joining the jihadist campaign. This would involve stronger border controls, more rigorous screening, cancellation of more passports, and co-ordination with tourist operators to prevent planes being used as terrorist weapons.

In a key development, five key Sunni-Arab states have openly supported the US bombing campaign in Syria, and US Secretary of State John Kerry has announced he has secured the support of "more than 50 countries".

Ms Bishop rejected a suggestion of doubts by Arab states.

"The foreign ministers that I've spoken to from the region, support it, they see that this ungoverned space in eastern Syria is a breeding ground for this type of terrorism and I've spoken to many foreign ministers from the region and they support the United States' efforts," she said.

Governments now hope to co-ordinate tougher measures to stop the flow of foreign fighters to the Iraq-Syria conflict and to other jihadist campaigns being waged in Africa and elsewhere.

Follow us on Twitter