Iran on Thursday warned the US president against any "adventurism" before leaving the White House, after Donald Trump said he would hold "Iran responsible" for any fatal attack on Americans in Iraq.

Foreign Minister Mohammad Javad Zarif's comments came after Trump accused Iran of being behind a rocket attack Sunday on the US embassy in the Iraqi capital, that caused material damage but no deaths.

The exchange also comes as tensions mount ahead of the first anniversary of the killing of top Iranian general Qasem Soleimani in a US drone strike in Baghdad.

Trump "uses a worthless photo to recklessly accuse Iran", Zarif said on Twitter Thursday, referring to an image Trump had posted after the embassy attack of three rockets he said had come from Iran.

"Trump will bear full responsibility for any adventurism on his way out," Zarif added.

Trump ordered a drone strike on January 3 this year to kill powerful Iranian general Soleimani while he was in Baghdad.

Days later, Iran launched a volley of missiles at Iraqi bases housing US and other coalition troops. Trump refrained from any further military response.

But the US leader, now in his final weeks in office, is sticking to his "maximum pressure" approach toward the Iranian regime.

"Now we hear chatter of additional attacks against Americans in Iraq," Trump tweeted Wednesday, before warning, "if one American is killed, I will hold Iran responsible. Think it over".

Zarif had responded earlier Thursday, tweeting, "Putting your own citizens at risk abroad won't divert attention from catastrophic failures at home."

The US embassy in Iraq and other foreign military and diplomatic sites have been targeted by dozens of rockets and roadside bomb attacks since late 2019.

The US diplomatic mission has already partially withdrawn its staff due to security concerns, two senior Iraqi officials told AFP earlier this month.