The call came after US President Donald Trump accused Iran of being behind Thursday's attacks on two oil tankers, the latest episode of worsening ties between Baghdad's two closest allies.

According to Abdel Mahdi's office, Pompeo phoned the Iraqi prime minister and discussed "the crisis between the US and the Islamic Republic of Iran."

Abdel Mahdi told Washington's top diplomat that Iraq was "striving for calm."

The prime minister has suggested Iraq as a potential mediator between the United States and Iran, but his offers have borne little fruit.

Thursday's twin attacks on two vessels after they passed through the Strait of Hormuz -- which Trump said had Iran "written all over it" -- have raised fears of conflict in the strategically vital waterway.

Iran has denied involvement and Foreign Minister Mohammad Javad Zarif accused the US of seeking to "sabotage diplomacy".

Iraq condemned the attacks but did not accuse any country of perpetrating them.

Abdel Mahdi earlier this week warned of the dangers of war.

"Iran isn't weak, and neither is the US. All sides know that war will cost a lot. No one wants war, but does that mean we have peace? No," he told reporters on Tuesday.

Baghdad has strong military and diplomatic ties to the US but it is also very close to Tehran, one of Iraq's top trade partners with sway over many Shiite armed units.

Iraq has thus been caught in the throes of the tug-of-war between Washington and Tehran since Trump last year withdrew from the 2015 nuclear deal and imposed tough sanctions.

Baghdad secured waivers from Washington to keep importing Iranian gas and electricity for its crippled power sector, but those exemptions will end in less than a week with no indication of whether the US has granted another extension.