Large numbers reportedly turned out in Rasht, in the north, and Kermanshah, in the west, with smaller protests in Isfahan, Hamadan and elsewhere.
Many angry demonstrators had protested in many cities across Iran on Thursday, including the second-largest city of Mashhad, over rising food prices and inflation. In Tehran, fewer than 50 people protested at a public square.
Thousands of Iranians took to the streets throughout the country on Thursday to protest against the deteriorating economic situation. The protesters also chanted, "We don't want the Islamic Republic", "death or freedom", "free all political prisoners", "we are going to take back our country".
Purely political protests are rare in Iran, where security services are omnipresent.
Mashhad government Mohammad Rahim Norouzian was quoted by IRNA as saying the protests were organized by "counter-revolutionaries".
The arrests were for "demolishing public property and lacking a permit for the protests", Mashhad's deputy attorney general, Hassan Heydari, told Tasnim. The last unrest of national significance occurred in 2009 when Mahmoud Ahmadinejad's re-election as president ignited eight months of street protests.
Iran police fire tear gas to dispel protesters in Tehran on Saturday
More provocatively, there were also chants of "Death to the dictator", and "Not Gaza, not Lebanon, my life for Iran" - a reference to anger in some circles that the government is focusing on the wider region rather than improving conditions at home.
Iran's senior vice-president Eshaq Jahangiri said Friday that some political factions are using the economy as an excuse to attack the government, pointing to external influences behind the protests.
Rouhani presided over a 2015 deal with world powers to curb Iran's nuclear program in return for the lifting of sanctions - moves which the International Monetary Fund (IMF) said recently had started an economic recovery although it was hampered by the urgent need to shore up banks.
Several provinces this week reported the price of eggs had risen by up to 50 percent, according to the semi-official Iranian Students News Agency.
Jahangiri called on the Iranian elites to reach consensus on the main problems that the country is facing today and added "to resolve the problems we need to allocate the required resources to bridge the current gap of social division and create consensus on the main issues".