Hundreds of Iraqis stormed the U.S. Embassy in Baghdad on Tuesday in the latest sign of trouble for the Trump administrations attempt to simultaneously thwart the Islamic State and Iran. Its fresh proof that President Donald Trumps 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 groups 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. didnt 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 Irans yearslong rivalry in Iraq. Trumps 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 thats 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.

The U.S. doesnt 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 hasnt 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 its 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 administrations top priority, officials seem convinced its 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 Irans 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.