Iran’s Islamic Revolutionary Guard Corps launched a missile attack late Tuesday against two Iraqi military bases housing U.S. troops.

In a statement, the Defense Department said, “It is clear that these missiles were launched from Iran and targeted at least two Iraqi military bases hosting U.S. military and coalition personnel at Al-Assad and Irbil.” The Pentagon said it was still assessing damage from the strike. No American casualties have been reported, as yet.

“So far, so good,” President Trump tweeted.

Tasnim News, an Iranian news outlet closely linked to the IRGC, published a statement from the IRGC which claimed it fired “tens” of rockets at al Asad air base in Iraq in an operation dubbed “Operation Martyr Soleimani.”

“We warn the Great Satan, the bloodthirsty and arrogant regime of the US, that any new wicked act or more moves and aggressions (against Iran) will bring about more painful and crushing responses,” the Guards wrote.

“ This is what we were afraid of. We were afraid we’d get pulled into this struggle between the U.S. and Iran. And now we are seeing it. ” — Kurdish member of parliament

The IRGC claimed the strike was the country’s “vengeance” for the assassination of former Quds Force commander Maj. Gen. Qassem Soleimani.

The operation follows a U.S. drone strike earlier this week which killed Soleimani, a powerful commander in Iran’s military and the officer in charge of Tehran’s wars in Iraq and Syria. The operation has plunged the U.S. and Iran into conflict after a summer which saw what the Trump administration said were escalating Iranian covert attacks against the U.S. and its allies in the region.

The Tuesday night strike represents a significant escalation of Iran’s own. Never before have the Iranians fired ballistic missiles, orders of magnitude more dangerous than rockets, at U.S. positions in Iraq—not during the 2003-2011 U.S. occupation, nor the return of U.S. forces to Iraq after 2014.

An Iranian official, apparently taunting Trump, tweeted out a picture of the Iranian flag immediately after the attack, mimicking Trump’s own American flag tweet posted in the immediate aftermath of Soleimani's killing.

The IRGC’s statement warned other countries housing U.S. military bases that they could become targets. In addition, the IRGC statement said: “By no means do we consider [Israel] separate in these crimes from the American criminal regime.”

But Javad Zarif, the Iranian foreign minister, sounded a somewhat softer tone. “Iran took & concluded proportionate measures in self-defense under Article 51 of UN Charter,” he tweeted. “We do not seek escalation or war.”

The IRGC-linked Fars News agency also published a video of what it said were rockets launched at Ain al Asad air base in Iraq, which is home to a small number of U.S. forces. The video shows what appears to be a handful of rockets streaking through the night sky.

The Pentagon said Iran’s attack included “more than a dozen ballistic missiles.” It’s unclear what kind of ballistic missile was used in the attacks but Iran’s missile arsenals include weapons which carry warheads weighing several hundred pounds in contrast to the smaller, unguided artillery rockets which the U.S. says Iranian proxy groups have used against American bases in Iraq over the past few months.

Meanwhile, on the ground in Iraq, officials in both Baghdad and Erbil scrambled to get details of the rocket attacks in both cities. Senior leaders seemed to be unaware of exactly how many rockets had fallen and if there was significant damage to American infrastructure or whether anyone had been killed.

Jennifer Carafella, the research director for the Institute for the Study of War, said that by targeting the base at Erbil as well as Al-Asad, the Iranians were sending a message to Iraq’s Kurds to dissuade them from permitting U.S. forces evicted by Baghdad to reposition north to Kurdistan.

“Iran is signaling to the U.S. that nowhere in Iraq is safe,” Carafella said, “and to the KRG [Kurdistan Regional Government] that there’s a price for standing by the Americans.”

“This is what we were afraid of,” said one Kurdish member of parliament. “We were afraid we’d get pulled into this struggle between the U.S. and Iran. And now we are seeing it.”

“The Kurds want U.S. troops to stay. They’ve always wanted U.S. troops to stay. But in this environment the Kurds are going to be asking for a lot more backing and confirmation that the Trump White House is going to have their back,” said a former senior Obama administration official working on Iraq policy.

“ In a classified briefing to congressional staff last week, U.S. officials indicated that the precision of missile strikes could point to whether or not Iran was escalating hostilities. ”

Throughout the course of the U.S.-led war on ISIS, the al Asad base was home to both American troops and military equipment, including MQ-9 Reaper and MQ-1C armed drones.

Unknown militants in Iraq attacked the base with smaller rockets in early December, shortly after Vice President Mike Pence arrived at the base for a visit.

In the three days following the strike on Soleimani, Predata—a firm that provides public and private sector clients insights based on public internet traffic data-monitored levels of online attention to hundreds of potential retaliation targets. One of the small number of trends that stood out was notably high levels of Persian-language attention to the al Asad airbase, according to Joel Meyer, a vice president at Predata. The firm is known for correctly predicting the timing of multiple North Korean ballistic missile tests.

In a classified briefing to congressional staff last week, U.S. officials indicated that the precision of missile strikes could point to whether or not Iran was escalating hostilities, according to multiple sources with knowledge of the comments. Iranian proxy forces have long harassed U.S. targets with rockets that miss their targets; using missiles with more sophisticated targeting systems would be an indicator of heightened aggression from the Islamic Republic. Rep. Michael Waltz appeared to allude to the same issue in a Fox News appearance after the strike on al Asad, saying a strike that didn’t result in casualties could be seen as de-escalatory.

—Spencer Ackerman and Betsy Swan contributed reporting