"The ministry regrets the American decision to pull its staff out of Basra," a statement said.

Secretary of State Mike Pompeo ordered all but emergency staff to leave Basra, with consular duties to be taken over by the embassy in Baghdad.

He blamed Iranian militias for "indirect fire" against the US consulate.

The State Department also sent out a renewed advisory urging Americans not to travel to Iraq.

Iran, for its part, rejected what it called the US "propaganda and false accusations", insisting it condemned any attacks on diplomatic sites.

"Iran sees the absurd US justification which follow weeks of propaganda and false accusations against Iran and Iraqi forces as playing a blame-game," said the country's foreign ministry spokesman Bahram Ghasemi.

"The Islamic Republic condemns any aggression against diplomats and diplomatic sites," he added.

Ghasemi charged that the US move was a pretext for promoting "insecurity in Iraq" and to "pressure the country's government."

Basra has been at the centre of protests that broke out in the southern province in July before spreading to other parts of the country, as demonstrators railed against poor services and condemned corruption among government officials.

Protesters have set fire to several government buildings as well as headquarters of political parties and militias backed by Iran, which saw its consulate in Basra burnt to the ground.

In Baghdad in early September, assailants fired three mortar rounds into the Green Zone, a heavily fortified area which is home to the Iraqi parliament, government offices and the US embassy.

The rare attack did not cause casualties or damage.

Neighbouring Iran is the other major outside power present in Iraq, alongside bitter foe the United States which led the 2003 invasion that toppled veteran dictator Saddam Hussein.