The Americans will leave one day, Quds Force commander General Qasem Soleimani once told Iraqi leaders, but Iran will remain Iraq’s neighbor. That lesson has only been reinforced by the lead role Iran has since taken in the fight against ISIS.

Iran aspires to Middle East hegemony and its foreign policy is designed to achieve that goal. We see this Iran’s support for Syria’s Bashar Assad, its support for Houthi rebels in Yemen, in nuclear negotiations with the West, and in its support for Iraqi forces against ISIS. Iran’s message is that it is in control and any decision of significance must go through Tehran.

Iran saw the power vacuum in Iraq left by Saddam Hussein’s 2003 defeat as an opportunity to expand its influence at the expense of the U.S. and other Mideast countries. Iran armed and supported Shiite militants fighting against the U.S. and exploited Iraq’s sectarian tensions. The U.S. pulled its remaining forces from Iraq in December 2011—a year after Soleimani orchestrated an Iraqi coalition government for Iraqi Prime Minister Nouri Maliki on the condition he insist all American troops leave the country. U.S. troops departed, but Iran remained. (Soleimani’s influence in Iraq was detailed in this January post.)

With the rise of ISIS, Soleimani and the Islamic Revolutionary Guard Corps (IRGC) are on the ground again in Iraq and Iranian leaders regularly praise their noble fight. The Iranians are supplying heavy weaponry to Iraqi forces, including Iranian proxies such as the Badr Organization. Soleimani is hailed as a hero in Iranian media and Iran is increasingly viewed as Iraq’s champion. In March, the New York Times described security checkpoints between Tikrit and Baghdad decorated with posters of Iran’s Supreme Leader Ayatollah Khamenei. For a country with designs on regional supremacy, this is prime propaganda material.

In December 2014, U.S. Secretary of State John Kerry called “the net effect” of Iran’s campaign against ISIS in Iraq “positive.” In the short term, this is true. ISIS represents a threat to regional stability and particularly to U.S. allies such as Egypt, Jordan, and Israel. In the long term, however, Iran is creating puppet strings throughout the region.

We are already seeing evidence of Iran’s political sway in Iraq. Nouri Maliki’s successor, Prime Minister Haider al-Abadi, recently criticized the Saudi campaign in Yemen, ignoring Iran’s interference in that country in support of Houthi rebels and questioning whether Saudi Arabia might invade Iraq next. “The idea that you intervene in another state unprovoked just for regional ambition is wrong,” he said. Without a broader context, one might think al-Abadi was talking about Iran, not Saudi Arabia.

Saudi Arabia is challenging Iran’s influence in Yemen by confronting the Iranian-backed Houthis. Iran has said it would use all of its influence—and it has a lot in the country, according to Iranian Foreign Minister Javad Zarif—to bring about a peaceful resolution to the conflict.

Unlike in Yemen, Iran’s presence in Iraq extends beyond its proxies. Iran has committed troops and its top general, Soleimani, to the fight against ISIS. In Iraq, the challenger to Iranian influence is the U.S., which is also fighting ISIS, but not by committing troops like Iran. Because of this, it is instead the highly visible Soleimani and the IRGC that are praised as Iraq’s saviors in local media.

Yemen and Iraq are pieces of the same puzzle that Iran hopes will come together to reveal Iran as being a stabilizing force in the Middle East. Barring a string of highly visible defeats of Iranian forces in Iraq, which would likely also strengthen ISIS, Iran’s influence in that country appears secure for the foreseeable future.

As Soleimani said, Iran will always be Iraq’s neighbor.