Both the US consulate in Iraq's third city Basra and its embassy in Baghdad were in areas that came under attack.

But the main target of the unrest in Basra were the offices of political parties and militias backed by Iran, which saw its consulate in the city burnt to the ground.

Iranian foreign ministry spokesman Bahram Ghasemi blamed the unrest on US support for "groups which have spread and promoted violence and extremism".

"The US government must be held accountable for its years of support for these groups," Ghasemi said, according to the semi-official ISNA news agency.

He was responding to a statement by the White House on Tuesday, which criticised Iran for failing to prevent the violence, particularly the attacks on the US diplomatic missions.

"Iran did not act to stop these attacks by its proxies in Iraq, which it has supported with funding, training, and weapons," the statement said.

Ghasemi described the statement as "astonishing, provocative and irresponsible".

"America should know that by playing such clumsy blame games, it cannot cover up the consequences of its wrong, fruitless and destabilising policies in the region," he said.

The rare attack on the US embassy in Baghdad came on Friday when three mortar rounds were fired at the capital's fortified Green Zone, though no casualties or damage was reported.

Bitter foes Iran and the United States are Iraq's principal allies and have long vied for political influence.

"A safe and developed Iraq has always been among the priorities of the Islamic Republic of Iran and conspiracies by third parties cannot prevent the enhancement of these long-standing and solid relations," Ghasemi said.