Following the “bitter” incident, “which was condemned by many of Iraq’s political and non-political figures, Iranian diplomats were immediately resettled in a new building and resumed their work,” ISNA quoted Foreign Ministry Spokesman Bahram Qassemi as saying on Tuesday.
The attack took place on Friday after the saboteurs entered the facility, which the Islamic Republic had leased from Iraq.
Tehran has urged Baghdad to pursue and punish the perpetrators.
Iraq’s Ministry of Foreign Affairs has condemned the attack.
The city of 2.5 million has been the scene of protests against mismanagement and poor public services since July.
Last week alone, at least 12 protesters were killed during scuffles with security forces and many of the city’s institutions were set on fire.
The violence has also featured instances of attempted infiltration into the oil production and processing facilities in the city.
On Sunday, Iraq’s Hashd al-Sha’abi said it had evidence showing that the United States diplomatic missions in the Arab country had instigated the violence in Basra.