One member of parliament told state broadcaster IRIB that there were three gunmen inside the parliamentary complex in central Tehran, armed with rifles and a pistol.
News agencies ISNA and Fars said three people had been shot, including at least one security guard.
An apparently coordinated attack took place at the mausoleum of Iranian revolutionary founder Ruhollah Khomeini, Fars reported.
IRIB and Fars said an armed man was inside the mausoleum in southern Tehran, around 20 kilometres from the parliament building, with reports of several injuries.
Iran provides key ground forces against IS and other rebel groups in Syria and Iraq.