Iranian President Hassan Rouhani phoned his French counterpart Emmanuel Macron on Tuesday to demand action against a "terrorist" Iranian opposition group he accused of fomenting recent protests.

"We criticise the fact that a terrorist group has a base in France and acts against the Iranian people... and we await action from the French government against this terrorist group," Rouhani told Macron, according to a report on Iranian state television.

He was referring to an exiled Iranian opposition group based in Paris and called the Mujahedeen-e-Khalq.

Iranian authorities accuse the group, which the regime describes as "hypocrites", of fuelling the unrest rocking the Islamic republic and of links with regional Sunni rival Saudi Arabia.

General Rassul Sanairad, a political deputy to the head of the powerful Revolutionary Guards, said Tuesday the Mujahedeen-e-Khalq had been instructed by the Saudi rulers and some European states to "create insecurity" in Iran, Tasnim news agency reported.

Nearly a week of unrest has seen 21 people killed and hundreds arrested in Iran, in the biggest test for the Islamic regime in years.

It began in second city Mashhad on Thursday and quickly spread to other towns and cities.

However, Tehran's deputy mayor said the city, which had witnessed small protests the past three nights, was calm on Tuesday night and no incidents had been reported, ISNA news agency said.