Iranian officials announced 40 rallies across the province of Tehran after Friday prayers, building on huge pro-government marches seen in many other cities over the previous two days.
The US imposed sanctions against five Iranian firms alleged to have been working on an illegal ballistic missile program, linking the move to the protests.
"These sanctions target key entities involved in Iran's ballistic missile program, which the Iranian regime prioritises over the economic well-being of the Iranian people," US Treasury Secretary Steven Mnuchin said.
There were some reports of small anti-government demonstrations in provincial towns, but these could not be verified.
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A total of 21 people died and hundreds were arrested in five days of unrest that began December 28 as protests over economic woes and quickly turned against the regime as a whole, with attacks on government buildings and police stations.
The UN Security Council was set to hold an emergency meeting on the issue later Friday at the request of the United States.
Iran's political establishment has closed ranks against the unrest, with even reformists condemning the violence.
But many have also called on President Hassan Rouhani to address the economic issues that drove the initial protests and parliament has already moved to block unpopular budget measures announced last month, including fuel price hikes.
"The people's main demand now is for the government and officials to deal with the economic problems," Ali Akbar Velayati, an adviser to supreme leader Ayatollah Ali Khamenei, told the semi-official ISNA news agency on Thursday.
Interior Minister Abdolreza Rahmani Fazli said 42,000 people had taken part in the unrest nationwide.
It was higher than a previous figure of 15,000 given by the head of the Revolutionary Guards, but still far below the hundreds of thousands that took to the streets during the last major protest movement in 2009.
A US State Department spokeswoman said those killed and detained "will not be forgotten", after the White House warned it could impose sanctions on any officials it holds responsible.
Iranian Foreign Minister Mohammad Javad Zarif tweeted back: "Trump has an odd way of showing 'such respect'."
"From labelling them a 'terrorist nation' and banning them from visiting the US, to petty insults on the name of the Persian Gulf," he wrote, referring to Trump's use of the term "Arabian Gulf".
Russia jumped to Iran's defence, with deputy foreign minister Sergei Ryabkov telling state agency TASS: "Despite the many attempts to distort what is really going on (in Iran), I am sure that our neighbour, our friend, will overcome its current difficulties."
Under the deal, Trump must actively lift certain sanctions every few months and the next deadline falls on January 12.
Iran -- which has long accused the United States and Sunni Arab rivals led by Saudi Arabia of interference in its affairs -- said external "enemies" were behind recent unrest.
Rouhani came to power in 2013 promising to mend the economy and ease social tensions, but high living costs and unemployment have left many feeling that progress is too slow.
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