Iranian authorities have threatened a crackdown against protesters and scrambled to block social media apps allegedly used to incite unrest as the biggest demonstrations in nearly a decade continued for a fourth day.

People across Iran took to the streets again on Sunday evening in defiance of a heavy presence of riot police and state warnings to stay away.

The demonstrations began over economic grievances on Thursday but have since taken on a political dimension, with unprecedented calls for the supreme leader, Ayatollah Ali Khamenei, to step down.

Iran’s president, Hassan Rouhani , in his first comments about the protests, aired on national television on Sunday night, said “people have the right to criticise”, but said the authorities would not tolerate antisocial behaviour. He said criticism was “different from violence and destroying public properties”.

Officials said they arrested at least 200 people during demonstrations in central Tehran on Saturday. It was not clear how many were arrested in the provinces, which saw protests on a bigger scale than the capital. Two protesters were killed in western Iran on Saturday.

The protests are the biggest in Iran since 2009, when demonstrators called for the removal of Mahmoud Ahmadinejad as president after what they regarded as his fraudulent re-election.

Videos posted on social media from Saturday night in Tehran showed protesters taking down large banners depicting the ayatollah’s image, in acts of resistance rarely seen since the 1979 Islamic revolution.

One video showed demonstrators taking down an image of the leader of Iran’s powerful Quds force, Qassem Suleimani, who is spearheading Iran’s involvement in regional affairs, particularly the war in Syria.

Rouhani, urging the nation to be vigilant, acknowledged that people were unhappy about the state of economy, corruption and a lack of transparency. “People are allowed under the constitution to criticise or even protest but […] in a way that at the end they lead to a better situation in the country for the people,” he said.

Condemning the US president, Donald Trump, who has voiced support for the protests, Rouhani said: “This gentleman who today sympathises with our people has forgotten that a few months ago he called us a terrorist nation. The one who has opposed the Iranian nation from his head to his toe has no right to express sympathy for people of Iran.”

On Sunday Trump tweeted that “people are finally getting wise as to how their money and wealth is being stolen and squandered on terrorism”, adding that the US was “watching very closely for human rights violations”.

Earlier in the day, Iran’s interior minister, Abdolreza Rahmani-Fazil, said authorities would not tolerate the “spreading of violence, fear and terror”, which he said would “definitely be confronted”.

“Those who damage public property, disrupt order, people’s security and break the law must be responsible for their behaviour and should answer and pay the price,” he said, according to the website of the state broadcaster Irib.

The broadcaster said authorities had blocked Instagram and the messaging app Telegram, which is the most popular social networking platform in Iran, citing an anonymous source who said the move was “in line with maintaining peace and security of the citizens”. Authorities said the filtering was temporary.

Telegram’s CEO, Pavel Durov, said it had blocked access to the popular Amadnews channel after it had “started to instruct their subscribers to use Molotov cocktails against police”.

A source in Iran told the Guardian the state had started blocking access to Telegram, but it was not covering all provinces yet.

Authorities said two protesters were killed in the western province of Lorestan on Saturday, but denied it was the result of clashes between demonstrators and riot police.

The deputy governor for Lorestan, Habibollah Khojastehpour, said police and security guards had not opened fire, and instead blamed “Takfiri groups” ? Iran’s term for Sunni extremists ? and foreign intelligence services. “Unfortunately in these clashes two citizens from [the city of] Doroud were killed,” he said.

Many senior figures within the reformist camp and the opposition Green movement remain perplexed as to how to respond to the current wave of unrest. The sharp nature of some of the slogans, which have challenged the foundations of the Islamic republic, has left them mute.

There have been anti-Khamenei chants such as “Death to the dictator” and slogans opposing Iran’s regional policy, including “Let go of Syria, think about us” and “I give my life for Iran, not Gaza, not Lebanon”.

There were also nostalgic slogans in support of the monarchy and the late shah, as well as some with a nationalistic nature, including “We are of Aryaee [Aryan] race, we don’t worship Arabs.” Relatively fewer chants were heard in support of two opposition leaders under house arrest, Mir Hossein Mousavi and Mehdi Karroubi.

Some videos showed protesters apparently setting bins on fire and trying to break into government buildings. The semi-official Tasnim news, which is close to the elite Revolutionary Guards, published a photo that it said showed a protester setting fire to the Iranian flag. There were chants of “Death to the Revolutionary Guards” in at least one city.

Many Iranians are sceptical about how the protests have spread so quickly. One prominent senior reformist commentator, Hamidreza Jalaipour, said reformists were opposed to protests instigated by “advocates of regime change”, implying that the new wave of protests was not spontaneous.

A protester from Tehran University told the Guardian by phone that although students were puzzled about how the protests were organised and spreading so quickly, they were not “getting leads from anyone”.

Ali Vaez, Iran project director at International Crisis Group, called the protests “an explosion of the Iranian people’s pent-up frustrations over economic and political stagnation”, but he said: “This is neither a revolution nor a movement.”

Vaez said: “Given its lack of leadership, organisation and mission, it is likely to peter out or will be quelled. The Rouhani administration has two options: it can follow the example of its predecessors ([Ali Akbar Hashemi] Rafsanjani after the protests of the early 1990s and [Mohammad] Khatami after the 1999 student uprising) and opt for a more cautious path, or capitalise on public discontent to push the system towards more genuine reforms. That choice will ultimately determine the Islamic Republic’s fate.”

Iranian conservatives, while acknowledging ordinary people were protesting for what they said were mainly economic reasons, accused foreign powers of inciting violence and exploiting the situation.