Iran's supreme leader Ayatollah Ali Khamenei delivers a speech during a ceremony marking the 25th death anniversary of Ayatollah Ruhollah Khomeini, founder of the Islamic Republic, in Tehran June 4, 2014. (Reuters)

President Obama left out one important element in his address on strategies to confront the Islamic State: How Iran fits in the emerging coalition.

It’s a question that can’t be set aside indefinitely, and could be among the defining challenges of the U.S.-led coalition. Like all affairs in Iraq – and neighboring Syria, for that matter – Tehran is in the mix either directly or as patrons for proxies.

It’s hugely improbable that Iran would fall in line as a reliable partner under an American umbrella. On Thursday, Iran’s Foreign Ministry said the international alliance against the Islamic State is "shrouded in serious ambiguities." The statement made no mention of Obama’s speech.

But Iran – with deep interests in both Iraq and Syria – has many reasons to also seek the Islamic State’s demise. In another of the Middle East’s strange-bedfellow outcomes, Iran is likely to be drawn into any Western-led scenarios against the Islamic State militants and their networks.

Here are five reasons why:

SHIITE MUSCLE: Iran has important sway over powerful Shiite militias in Iraq. Some had turned their guns against American troops in the past. Now, units of Shiite fighters have joined the battles against the Sunni-led Islamic State in northern Iraq. The reason is balance of power. Iraq’s Shiite factions – and, by extension, Iran – are deeply unsettled by the idea of rising Sunni extremists who condemn Shiite Muslims with the same fervor they denounce the West.

POLITICAL POWER: The Shiite-led government in Baghdad remains firmly in Tehran’s orbit. Iran was closely intertwined with the leadership of former Prime Minister Nouri al-Maliki. That is unlikely to change significantly under the newly named Prime Minister Haider al-Abadi despite his greater outreach to the country’s minority Sunnis. Any comprehensive plan for airstrikes or other attacks on the Islamic State must get at least some nod from Baghdad. And that means Iran always is in the wings.

SYRIA: The fight against the Islamic State must eventually cross the border to Syria, where the militants have important strongholds. Here’s where it gets really complicated. Obama had suggested that the ground game in Syria could be led by "moderate" rebels whose main goal – until now – has been trying to topple Syrian President Bashir al-Assad. Iran remains a critical ally of al-Assad. The West doesn’t want to deal directly with al-Assad to coordinate any strategies. But Iran could emerge as an intermediary.

REGIONAL RIVALRIES: Washington and its allies want as few Middle East distractions as possible. This includes trying to keep a lid on the always-simmering rivalries between Iran and Sunni power Saudi Arabia, a Western ally whose strict brand of Islam also has provided ideological grounding for some extremists. Before his speech, Obama called Saudi Arabia’s King Abdullah. It's another sign of the critical Saudi role in mobilizing Arab support to root out the Islamic State. Another message is on Washington’s mind: Keeping Saudi Arabia calm amid possible greater outreach to Iran. Saudi Arabia threw a tantrum when America opened nuclear talks with Iran and made overtures for more dialogue. The United States doesn’t want another Saudi spat on its hands now.

ROOM TO TALK: There are more chances than ever for direct U.S.-Iran dialogue. Channels have been open through the negotiations over Tehran’s nuclear program. Tehran and Washington also have taken part previously in three-way talks hosted by Iraq. Later this month, the world’s leaders will be in New York for the biggest diplomatic talkfest of them all: the United Nations General Assembly.