Two people were shot dead in protests in Iran bringing to four the number of fatalities in the country's most serious unrest since 2009 as messages on social media called for more anti-government demonstrations on Monday.

The two were killed on Sunday in the southwestern town of Izeh and several others were injured, ILNA news agency quoted local member of parliament Hedayatollah Khademi as saying.

'I do not know whether yesterday's shooting was done by rally participants or the police and this issue is being investigated,' Khademi was quoted as saying.

Messages on social media urged Iranians to hold rallies in the capital Tehran and 50 other urban centres, many of which have already seen four days of unrest since price protests in the second largest city Mashhad on Thursday turned political.

Protests continued overnight even though President Hassan Rouhani appealed for calm. He said Iranians had the right to criticise authorities but warned of a crackdown against unrest.

'The government will show no tolerance for those who damage public properties, violate public order and create unrest in the society,' Rouhani said in remarks carried by state TV.

Tens of thousands of people have protested across the country against the Islamic Republic's government and clerical elite, prompting authorities to warn of a tough crackdown.

Security forces have showed restraint, hoping to avoid and escalation of the crisis triggered by economic hardships and corruption. Anger soon turned to Iran's clerical establishment in power since the 1979 revolution.

Some called on Supreme Leader Ayatollah Ali Khamenei to step down and chanted against a government they described as thieves.