President Trump is warning Iran that if they want a fight, it would be the "official end" of Iran. His threatening tweet came after a rocket landed near the U.S. embassy in Baghdad on Sunday. No one was hurt, and no group has taken responsibility. Iraqi authorities are searching for whoever fired the rocket.

With his country caught in the middle of a growing crisis, Iraq's President Barham Salih told CBS News correspondent Roxana Saberi that he's talking to both the United States and Iran to keep Iraq from becoming a battleground.

Iraqi President Barham Salih.

"Iraq has been living through hell for the last four decades," Salih said. "Enough of wars, enough of conflict. And certainly, Iraqis do not want to see this country yet again turn into a zone of proxy conflict."

Iraq is in a tough spot, hosting more than 5,000 U.S. troops, while also depending on local militias – many backed by Iran – for security.

The Trump administration says there's a heightened threat that some of those armed groups could turn their guns on American forces.

President Salih expressed concern that tensions between Iran and the U.S. could boil over into a war in Iraq? "Obviously we're very concerned. These tensions are extremely disconcerting in Iraq and in the neighborhood."

To defuse these tensions, Salih met last night with Iraqi political leaders, some linked to the pro-Iranian militias.

"I'm not saying there aren't groups beyond those who gathered here last night who may not be totally accountable to the state," Salih said.

Saberi asked, "Are you basically saying these militias that help Iraq fight ISIS, these militias – some of which are aligned with Iran – are answering to Iraq, but there may be rogue elements which are trying to provoke U.S. forces here?

"We do have problems with some rogue elements," Salih said, "and the government is intent on putting those people under control."

"Have you basically sent a message to cool it?"

"Absolutely," he said. "We are telling everybody, cool it. This is not the place to have your battles on."

It was a message he also shared with U.S. Secretary of State Mike Pompeo, who made a last-minute visit to Iraq earlier this month. Pompeo also said he asked Iraq to adequately protect Americans in this country.

"I think the Iraqi government is doing a lot in order to provide the necessary protection," Salih said.

Saberi asked, "Why do you think then that America ordered a partial evacuation of its embassy?"

"We were not happy with that," he replied. "We thought it was unwarranted, but we don't want to second-guess the U.S. government."

The Iraqi president also warned that in any conflict, ISIS could benefit: "While the tensions between the United States and Iran rage, we should not lose focus the real priority in this neighborhood, that is, combating terrorism. ISIS has been defeated territorially."

"So, this could be a distraction?" asked Saberi.

"Of course. No doubt about it."

President Salih said authorities have made progress identifying who was behind last night's rocket attack. But last night, the dust had hardly settled when the State Department released a statement, saying, "We will hold Iran responsible if any such attacks are conducted by its proxy militia forces." So, the tension in Iraq is ratcheting up.