Hundreds of Iraqis stormed the U.S. Embassy in Baghdad on Tuesday in the latest sign of trouble for the Trump administration’s attempt to simultaneously thwart the Islamic State and Iran. It’s fresh proof that President Donald Trump’s reliance on saber-rattling instead of diplomacy risks greater chaos in the Middle East — and his approach threatens the gains the U.S. has made there in recent years.

Demonstrators at the embassy ― the United States’ largest diplomatic facility ― chanted “death to America,” according to reports from the ground. They were supporters of an Iran-backed militia called Kataib Hezbollah that has significant influence inside Iraq. The U.S. hit some of the group’s camps on Sunday, killing 25 of its fighters, after blaming it for an attack on Friday that killed an American contractor and linking it to a spate of other flare-ups. Iraqi security forces ― who work with Iran and the U.S. ― didn’t stop the protesters’ approach but ultimately intervened to push them out of the compound as American diplomats huddled in a safe room and military personnel watched from rooftops with weapons drawn, per The Washington Post.

The crisis reflects a real and worrying escalation in the U.S. and Iran’s yearslong rivalry in Iraq. Trump’s decision to launch the strikes on the Iran-backed forces was a turning point, experts said. They were the first confirmed American response to Iranian pinpricks in Iraq and other arenas like the Persian Gulf since the summer, and represented a significant show of force to Tehran that some national security pundits saw as necessary and valuable. But they also challenged Iraqi sovereignty, reigniting resentment dating back to the 2003 invasion and presenting Washington as a threat to a growing wave of Iraqi nationalism that’s won mass support among citizens tired of the status quo. That response makes it harder for the U.S. to operate in Iraq, which in turn serves the interests of Iran and ISIS, already regrouping in Iraq, with no clear American gain.

Even with the immediate danger defused, along with a feared repeat of the 1979 Tehran hostage crisis, the events of the past few days suggest more danger lies ahead in Iraq, where there are currently 5,000 American troops. The president and his Senate allies Lindsey Graham (R-S.C.) and Tom Cotton (R-Ark.) reacted with anger on Twitter, warning of greater U.S. action against Iran, which Washington is already subjecting to “maximum pressure.” Kataib Hezbollah said demonstrations will continue until the embassy is closed.

America has locked itself into an escalation spiral. Randa Slim, senior fellow at the Middle East Institute

The U.S. doesn’t appear likely to shift its strategy away from bluster toward a savvier accounting of how Baghdad and Tehran are likely to operate. And without a move toward smarter engagement, Trump is stuck on a path that at best requires frequent tactical shifts without strategic progress, and at worst could entail major new bloodshed for Americans, Iraqis, Iranians and others in a region that hasn’t recovered from the onslaught of ISIS.

“The net result, whatever happens next, is reduced American prestige in Iraq,” Daniel Serwer, a Johns Hopkins University professor and former State Department official who worked on Iraq at the U.S. Institute for Peace, told HuffPost via email.

The U.S. has little ability to shape developments after the incident, said Randa Slim, a senior fellow at the Middle East Institute think tank.

“America has locked itself into an escalation spiral which it could not avoid after 11 attacks on its facilities in Iraq,” she wrote in an email. “The Iraqi government, which could have de-escalated tensions early on by clamping down on the militia activities, has proven to be unwilling and incapable to do so. The next move is in the hands of the Iraqi militias and their Iranian director.”

Now that the U.S. has signaled that it’s willing to deal with its concerns militarily, American policymakers may feel they need to constantly demonstrate even greater strength.

Because toughness toward Iran is the Trump administration’s top priority, officials seem convinced it’s worthwhile to treat U.S. interests ― and vulnerabilities ― in Iraq as a secondary concern, a choice that makes incidents like the embassy assault more likely. And unlike under the Obama administration, when Washington and Tehran had an unprecedented dialogue they used to manage potential crises, American officials presently have few ways to communicate with Iranian counterparts to prevent open conflict.

From Iran’s point of view, violence may seem like the best or only way to send a message. “Iran needs to increase the costs to the U.S. of its maximum pressure strategy,” Slim said. “Iraq and Syria are the proxy theaters where both countries have forces and where Iran can try to rebalance the power equation in its favor.”

Wissm Al-Okili / Reuters Demonstrators and militia fighters throw stones toward the U.S. Embassy in Baghdad on Dec. 31 during a protest to condemn airstrikes on bases belonging to Hashd al-Shaabi.

The Trump administration could have chosen a diplomatic approach, said Scott Anderson, a former State Department official and current Brookings Institution fellow. Officials might have tied their outrage over the contractor’s killing to Iraqis’ anti-Iran anger and strongly pushed Baghdad to rein in Iranian proxy forces. That would have denied Tehran the opportunity to present America as an aggressor and boosted skepticism of Iran’s role in the country.

The embassy attackers were separate from nationalist demonstrators against corruption and Iranian interference in Iraqi politics who have faced violent retaliation from the government and were holding their own rally on Tuesday.

Trump did post a message on Twitter expressing empathy for those protesters. Yet the overall impression since the weekend remains one of foreign hubris.

“Until now the focus of anti-government demonstrations had been against Iran, with the Americans relatively unscathed,” Serwer wrote. “Iraqis however will object to whoever violates their sovereignty. This time it is the Americans.”

Iran couldn’t have hoped for more, according to Anderson.

“Hawkish senators may be pleased by the toughness of Trump’s military response — but it’s hard to see how it aids U.S. interests,” he wrote on Twitter. “This was an old, familiar trap — and the Trump administration stepped right into it.”

The U.S. now plans to send additional forces to Iraq, Defense Secretary Mark Esper announced after the attack.