One member of parliament told state broadcaster IRIB that there were four gunmen inside the parliamentary complex in central Teheran, armed with rifles and a pistol.
News agencies ISNA and Fars said three people had been shot after the gunmen entered via the north entrance, including at least one security guard.
An apparently coordinated attack took place at the mausoleum of Iranian revolutionary founder Ruhollah Khomeini, several news agencies said.
An armed man had entered at the western entrance of the mausoleum and opened fire before blowing himself up with a suicide vest, the site’s head of public relations Ali Khalili told the IRNA news agency.
The mausoleum is in southern Teheran, around 20km from the parliament building.
The ILNA news agency said five people had been injured and that security forces were dismantling a bomb inside the mausoleum.
There were conflicting reports from inside the parliament complex, with some reports saying the situation had been brought under control while others said the shooting was continuing, with the buildings under lockdown.
ISNA reported that the shooters had been surrounded but had yet to be arrested.
Shiah Iran has been singled out as a target by Sunni jihadists, including the Islamic State group, but has largely escaped attacks within its urban centres.
Iran provides key ground forces against IS and other rebel groups in Syria and Iraq. — AFP