The Iranian employees had withdrawn from the building to safe places before the attack the source said on condition of anonymity Xinhua news agency reported.
The Iraqi Foreign Ministry later strongly regretted protesters attack on the Iranian consulate saying "it is an unacceptable development and is not in line with national hospitality for (diplomatic) missions " according to a statement by the ministry spokesman Ahmed Mahjoub.
"Targeting the diplomatic mission harms the interests of Iraq and its relations with other countries and does not relate to the slogans of demonstrations and their demand for services and water " Mahjoub said.
The demonstrators headed toward the US consulate but the attempt was unsuccessful because of upgraded security measures the source said.
Protesters also attacked a headquarters of the Iran-backed Asa ib Ahl al-Haq militant group and set fire to its building in Bareiha area in central Basra incurring heavy gunfire from the group s fighters the source said.
Asa ib Ahl al-Haq or League of People of Righteousness is part of the Hashd Shaabi brigades. The group was allegedly funded trained and armed by Iran s Quds Force during the U.S. occupation of Iraq and later became allied to the Shiite-led government.
Witnesses said the demonstrators set fire to the gate of the Presidential palace complex at the edge of the city which includes houses of local top officials and some bases of paramilitary Hashd Shaabi brigades.
Meanwhile Qais al-Khaz ali head of Asa ib Ahl al-Haq group threatened to "intervene strongly" if "things reach to the level that threats the existence of the state."
"Burning the headquarters of Asa ib Ahl al-Haq and some parties in Basra is political motivated and has relation with the power struggle in Iraq " Khaz ali said in an interview with a local television.
The demonstrations are part of days-long protests in the southern oil-hub province of Basra during which hundreds of angry demonstrators burned the provincial government buildings and offices of leading political parties and headquarters of some Shiite militias in protest of wide-spread corruption and water contamination in the province.
Basra the province s capital city which bears the same name has long witnessed complaints among its over 2 million residents about the collapsing infrastructure power cuts and corruption.
Water supply in the province is also widely criticized for high salinity with thousands of residents having been hospitalized.
The protesters also accused the influential political parties of being behind the wide-spread corruption which led to high unemployment and failure in rehabilitation of the country s electricity water and other basic services.
--IANS pgh/
