Even with the violent assault on the United States embassy compound in Baghdad on Tuesday, for which he threatened Teheran with a "very big price" to pay, and even as the Pentagon acted swiftly to reinforce deployment in the region, US President Donald Trump indicated that the US will exercise restraint.

The US president said he wants peace as much as the Iranians do, and doesn't see a war with Iran happening.

While such restraint certainly is laudable and conducive to cooling things down a bit, it doesn't suffice for meaningful headway to be made in unraveling the present impasse in the region.

Tuesday's storming of the embassy compound no doubt marks "increased threat levels against US personnel and facilities," as US Defense Secretary Mark Esper observed. But deploying more troops alone can't address the troubles in Washington's face.

Unless the real lesson is learned and taken to heart, unless Washington gives more thought to non-military options, and engages local players in a more constructive manner, there is little chance it will easily emerge from being mired in the Middle East.

Even though an outright war between the US and Iran may be ruled out for now, what is widely seen as proxy wars between the two parties may drag on, weakening both and worsening security conditions throughout the region.

The Tuesday attack in itself is an example of the complicated and thorny nature of the troubles at Washington's hand.

The embassy breach was carried out by members of Hashd Shaabi, an umbrella group formed by Iraq's paramilitary Kata'ib Hezbollah and other Iraqi Shiite paramilitary groups, allegedly Iran-backed, who lost 25 comrades in US airstrikes on Sunday in Iraq and Syria.

Those strikes — the largest of their kind in recent years — were allegedly in retaliation for recent attacks on US targets in Iraq, which Washington blamed on Iran as the orchestrator, although the latter denied the charge.

While the strikes also invited angry responses from Iran and Syria, it is the response from Baghdad which makes things worse. Calling them "flagrant violation" of its sovereignty, the Iraqi government said it would reconsider relations with the US-led coalition.

As some US observers have pointed out, the strikes turned some of the Iraqi anger away from Iran toward the US, which will in turn undermine US influence as well as its position in dealing with Teheran.

If Iran does have a role here, the outrage seen on Tuesday again showed the US president's "maximum pressure" tactic is not working. Instead, it is simply creating more problems than it solves.