Demonstrations started in the north-east as an outcry against economic hardship but turned political in many areas and saw some people chanting slogans against Supreme Leader Ayatollah Ali Khamenei, President Hassan Rouhani and Iran's foreign policy.
Government officials have said the protests are part of a wider attempt by Rouhani's opponents to discredit his leadership.
US President Donald Trump weighed in on the protests, saying "oppressive regimes can not endure forever".
In a tweet on Sunday, Amir-Abdollahian told Trump: "Do not get excited".
"This man, who is an enemy of the Iranian nation from the top of his head to his very toes, has no right to sympathise with Iranians", he added.
Trump's tweets the previous day angered Iran's government, leading the Foreign Ministry spokesman to say the "Iranian people give no credit to the deceitful and opportunist remarks of US officials or Mr. Trump". Protesters first took aim at rising food prices and corruption, driven partly by a sense that the July 2015 nuclear deal hasn't delivered the broad economic recovery many were expecting.
The "temporary" restrictions on the apps Telegram and Instagram were imposed to "maintain tranquillity", state news agency Irib reports. The Telegraph has changed her first name for security reasons.
Facebook, which owns Instagram, did not immediately respond to a request for comment.
Ahmad Khatami, a hardline cleric who leads Friday prayers in the capital Tehran, said the protests were similar to those in 2009 over alleged electoral fraud.
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Users said Sunday that they could no longer access the app via cellphone networks, though it was still available via Wifi and home internet connections.
Videos shared on social media showed thousands marching in towns and cities throughout Iran overnight.
The Foreign Ministry in Tehran dismissed Trump's comments, saying "the Iranian people place no value or credibility in the opportunistic claims of USA officials or of Mr. Trump himself".
"Some meant to enter and damage some government places but the attackers did not manage to achieve their goals. and the town is under control", the unidentified official told the ILNA news agency.
There were outbreaks of clashes in several cities on Saturday and two protesters died of gunshot wounds in the western city of Dorud.
He said "two of our dear Doroudi citizens were killed", without elaborating on the cause of death.
But local news reports said he also exhorted Iranians not to resort to violence, after reports of protesters attacking banks and municipal buildings across the nation, including a local government building in Tehran.
The protests have expanded to cities across the Islamic Republic in the days since.