On Monday, a crackdown by the government and security services was building, and riot police officers with water cannons were out in full force in Tehran, the capital.
The death toll from the clashes was up to at least 12, and in the central province of Esfahan, one police officer was reported killed and three wounded in a gunfight. “An agitator exploited the current situation, and using a hunting rifle, opened fire on police forces,” state television reported.
In all, about 200 people have so far been arrested in Tehran alone since the protests began Thursday, one security official told Iran’s ISNA news agency. There were arrests in provincial towns as well.
Mr. Rouhani has urged demonstrators to avoid violence but defended their right to protest. He did so again on Monday on Twitter.
“People want to talk about economic problems, corruption and lack of transparency in the function of some of the organs and want the atmosphere to be more open,” he wrote. “The requests and demands of the people should be taken note of.”
The protests are not just the largest in Iran since 2009. They also suggest a rejiggering of some traditional divisions.
People who live in rural provinces long viewed as supporters of the authorities are now leading most of the demonstrations. And while people in Tehran have also taken to the street, the capital is not the epicenter of the protests, as it was during the so-called Green Movement in 2009. In Tehran, many middle-class Iranians share the discontent but also fear insecurity.
The frustrations that led to the protests also appear different from the sentiments in 2009.
That year, a wave of demonstrations broke out after the contested election of a hard-line president, Mahmoud Ahmadinejad, and then turned into a wider protest movement against Iran’s leaders.
This time, it is the failure of President Rouhani, a moderate, to deliver greater political changes and economic opportunity, despite the lifting of some of the sanctions against Iran as part of the nuclear deal. Young people are especially angry. The average age of those arrested is under 25, one official said.
The poor economy especially affects Iran’s young people — more than 50 percent of the population is under 30, according to official statistics. Officially, youth unemployment is near 20 percent, but experts say it is really closer to 40 percent.
When the protests started last Thursday in the city of Mashhad, demonstrators chanted slogans about the weak economy.
But as the protests spread, they have taken on a far more political cast. Increasingly, they are being directed at Iran’s entire political establishment. Some demonstrators have even called for the death of Mr. Rouhani and of the supreme leader, Ayatollah Ali Khamenei.
The strength and volatility of the protests have caught Iranian politicians by surprise. Some have denounced them as “riots,” while others have acknowledged that the widespread frustrations at their root can no longer be ignored.
On Monday in Tehran, the atmosphere was tense and security forces were out in large numbers. Protest occurred sporadically, with people shouting slogans and leaving. The day before, protesters in provincial towns tried to storm police stations, military and installations, and also attacked a seminary, state television reported, showing footage of burned cars and fires.
Protests have taken place in at least half a dozen cities, including Karaj, Qazvin, Qaemshahr, Dorud and Tuyserkan, it said.
Access to the Telegram messaging app and the Instagram photo and video sharing app continued to be blocked by the authorities, cutting of the main communication tool for protesters. Special software used to circumvent the government filters could still be downloaded easily. And on Monday, as on other days, there were calls for protests online and on foreign-based Persian-language satellite channels.
Some residents said they were determined to continue the demonstrations, and several hundred gathered at central squares.
While the numbers of protesters in Tehran was small on Monday, the discontent was widespread. Many people on the streets complained about high prices, corruption and lack of change.
“We need to improve our economy, and the people’s voices must be heard,” said a 28-year-old woman, a piano teacher in Tehran, who asked not to be named out of fear of repercussions. “I’ll go out tonight again.”
Many youths in larger cities enthusiastically voted for Mr. Rouhani when he was re-elected in May, raising expectations among many in the reform camp. But since then even many of the president’s supporters say he has failed to fulfill his promises for improving an economy sorely hobbled by years of sanctions, corruption and mismanagement.
Even the lifting of economic sanctions under Iran’s 2015 nuclear deal with large foreign powers including the United States has not unleashed the growth Mr. Rouhani had hoped for, as key sectors of the economy remain under the thumb of obscure powers, including religious foundations and the country’s Revolutionary Guards. There is mismanagement and widespread corruption in all levels of the state apparatus.
Beyond that, the United States has continued other sanctions, making it still harder for Mr. Rouhani to make gains.
The economic frustrations do not appear to have been offset by the greater social freedoms that the president has granted young people. Under Mr. Rouhani, strict Islamic rules have been somewhat relaxed. Concerts have been allowed, and the morals police are largely off the streets. Illegal parties are usually no longer raided, although there have been exceptions.
But there is a wide gap between Iran’s changing and modernizing society and Iranian leaders who insist on keeping up their anti-Western policies and the state interpretation of Islam.
Mr. Rouhani’s decision not to include any women in his cabinet and his failure to put the relaxation of the rules into law have made many bitter.
The president has complained that power centers dominated by hard-liners have blocked many of his plans and decisions. Now, some protesters are venting their frustrations at the political and clerical establishment.
In Takestan, west of Tehran, several people were arrested after attacking a seminary, the Iranian news media reported. In Karaj, also close to Tehran, a gas station was burned, a witness reported.
Earlier on Monday, the semiofficial ILNA news agency quoted Hedayatollah Khademi, a representative for the town of Izeh, in Iran’s oil-rich but poor Khuzestan region, as saying two people had died there on Sunday night. He said the cause of death was not immediately known.
State television announced that 10 people had died on Sunday, but did not provide a location. “Some armed protesters tried to take over some police stations and military bases but faced serious resistance from security forces,” a presenter said.
“Illegal protests continued last night in several cities with less protesters participating, but they were as violent and turbulent, making residents of these cities concerned about their and their businesses’ security,” the state television report said.
The videos showed burned cars, fires and wreckage on the pavement. The report also showed a fire-brigade vehicle that was said to have been seized by protesters in Dorud, Lorestan Province.
By Monday evening, riot police officers belonging to the Islamic Revolutionary Guards Corps waited in an alley near Tehran’s city theater for a potential protest to start, as men and women anxiously walked the sidewalks. Others, families and couples, cruised around the area in cars. Many were young people.
“They want to start, but there is too many police,” one taxi driver said, looking at hundreds of people, and even more security forces. Plainclothes officers on motorcycles zipped by. Buses stood ready to take potential troublemakers into custody.
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