DAVOS (BLOOMBERG) - President Donald Trump acknowledged that Americans were hurt in an Iranian missile barrage to retaliate for the US killing of a top general, and said the injuries were "not very serious".

"I heard they had headaches," Mr Trump told reporters on Wednesday (Jan 22) during a press conference at the conclusion of a two-day trip to the World Economic Forum in Davos, Switzerland.

"I can report it's not very serious."

Mr Trump said he learnt of the injuries among US service members days after the Iranian counterstrike against US bases in Iraq in retaliation for the killing of Major-General Qassem Soleimani on Jan 3, which inflamed tensions between the US and Teheran.

Mr Trump's comments - in response to a reporter's question - followed a bilateral meeting earlier on Wednesday with Iraqi President Barham Salih on the sidelines of the Davos summit.

Tensions in the region were largely left on the back burner during Mr Trump's event in Switzerland, where the US President has focused on touting his economic record as counter-programming to the Senate impeachment trial that got under way in Washington this week.

Maj-Gen Soleimani's killing in Baghdad earlier this month prompted calls from Iraqi lawmakers for US troops to leave the country, but Mr Trump said he'd only do so if Iraq repaid construction costs related to a joint airbase.

An Iranian counterstrike didn't kill any Americans, but experts have warned about the possibility of retaliation from Iranian proxy groups.

As tensions simmer, Mr Trump has pushed to put new pressure on Iran and called on allies to abandon the 2015 Iran nuclear deal and to send more soldiers to Iraq, after Maj-Gen Soleimani's death led to calls for US withdrawal there.