A Baghdad court has issued a warrant for the arrest of US President Donald Trump as part of its investigation into the killing of a top Iraqi paramilitary commander.

Abu Mahdi al-Muhandis, the deputy head of Iraq's largely pro-Iran Hashed al-Shaabi paramilitary network, died in the same US drone strike that killed storied Iranian general Qasem Soleimani at Baghdad airport on January 3 last year.

The strike on their motorcade was ordered by Trump, who later crowed that it had taken out "two (men) for the price of one".

The UN special rapporteur for extrajudicial, summary or arbitrary executions, Agnes Callamard, has described the twin killings as "arbitrary" and "illegal".

Iran already issued a warrant for Trump's arrest in June, and asked Interpol to relay it as a so-called red notice to other police forces around the world, a request that has so far gone unmet.

The court for east Baghdad issued the warrant for Trump's arrest under Article 406 of the penal code, which provides for the death penalty in all cases of premeditated murder, the judiciary said.

The court said the preliminary inquiry had been completed but "investigations are continuing in order to unmask the other culprits in this crime, be they Iraqis or foreigners."

In the run-up to Sunday's anniversary of the twin killings, pro-Iran factions stepped up their rhetoric against Washington and Iraqi officials deemed to have colluded with it.