Since ISIS (the Islamic State of Iraq and Syria) intensified its land-grab across Iraq and Syria in early June, foreign powers have been drawn into the fight against the Sunni militant group. On Monday it formally declared a Islamic caliphate over its terrain, a proto-state governed by strict Islamic law.

It’s a complicated web. In the last two weeks, Iran has said it is ready to further boost Iraq’s Shiite-led government with military support. Syria’s President Bashar al-Assad bombed ISIS targets in Raqqa and along the Iraqi border. Hezbollah, the pro-Assad Lebanese group, said this week that it was prepared to fight “five times harder” against ISIS in Iraq than it already has in Syria. As a result, ISIS declared war on Hezbollah.

Then there are its foes outside the Iran-Syria-Hezbollah alliance. Earlier this week, U.S. President Barack Obama asked Congress for an additional $500 million to arm and train moderate rebels, who have been fighting against ISIS. American allies like Jordan and Saudi Arabia have a significant strategic interest in stemming ISIS, which now holds terrain uncomfortably close to its borders.

We asked Matthew Levitt, the Fromer-Wexler fellow and director of the Washington Institute’s Stein Program on Counterterrorism and Intelligence, to weigh in on the prospects of foreign intervention to check ISIS, particularly the chances that the U.S. will get further involved.

Syria Deeply: How concerned is ISIS right now about intervention by foreign powers?

Matthew Levitt: I can’t imagine that ISIS thought it would take over huge swaths of a country that was functioning – unlike Syria – and there wouldn’t be concern in both the [Arab] region and the West. What you have is the influx of Shia militias, support from Iran and a tremendous number of arms, and intelligence cooperation with the West on the part of both Iraq and Iran.

There’s a reason why ISIS was kicked out of al-Qaida, and why it’s considered more radical than al-Qaida. They believe that al-Qaida is sitting on the sidelines, not doing what has to be done. They also feel that in Iraq, there is an opportunity [for power] because the central government, which is Shia-dominated, has created problems for the Sunnis. ISIS takes solace in the fact that it has cooperation from tribes, and that some in the Gulf have been referring to events in Iraq as an intifada. There was a Saudi journalist who referred to what was happening in Iraq as “the wrong people doing the right thing” – that the Sunnis, in other words, should be rising up, and other Sunnis should be supporting them, but ISIS is the wrong group to [lead] this.

Syria Deeply: What about a U.S. intervention? At this point, the U.S. line is less hawkish than it has been in crises in Iraq in the past.

Levitt: Most people in the region across the spectrum look at the U.S. today and see a country and an administration that is looking to get out of conflicts, not get back into them. They’ve heard Obama say that he wants to avoid making mistakes, and the way to make mistakes is to get involved in military conflicts. I think they look at the red line fiasco in Syria and see a United States that is not necessarily willing to enforce its own red lines.

So I think they probably understand that the U.S. will take some action – and they’re probably concerned by reports that there are armed drones flying above Iraq and that there are significant naval assets in the region and increased intelligence cooperation – but I don’t think that they are losing sleep over a massive U.S. military bulldozer coming in. And that factors significantly into their calculus.

Syria Deeply: Right now, which foreign power is of the biggest worry to ISIS?

Levitt: I don’t know if its fair to say biggest. They don’t want to see Iran coming in in a huge way. And the Iranians are weary of coming in in a huge way, because they don’t want to make this into a sectarian conflict. The government of Iran has been clear that they don’t see this as a sectarian conflict. Iran does not want Iraq to break up. They want a unified Iraq that is dominated by Shia that are close to Iran.

I think that in some way [ISIS] is scared of the U.S. more, theoretically [based on past U.S. involvement in Iraq], but they don’t think it’s likely that the U.S. would, under its current leadership, be likely to engage [in a major way]. They’re not happy about the U.S. sending small numbers of forces to guard the embassy, or advisers, but it’s not going to make a difference for them.

Syria Deeply: Iran is reportedly scrambling forces to defend Baghdad. How important to ISIS is Baghdad at this time?

Levitt: Ultimately it’s a prize, but it’s a majority Shia city, it’s well defended, it’s clearly a red line for the international community, and ISIS has got plenty to do elsewhere in the country, right up to Baghdad’s front step. You never know with a group like ISIS, which puts ideology before tactics and strategy. And so you could have some effort to do something in Baghdad before ISIS is really ready. But I don’t think that in the immediate future, Baghdad is all that critical to them.