By Laura Smith-Spark, Dakin Andone and Jennifer Hauser, CNN

(CNN) -- Several Iranians were shot during protests late Saturday, a source tells CNN, after Iran's government warned citizens against holding "illegal" public gatherings, following two days of rare anti-government protests that spread to a number of cities.

One local source told CNN that during protests in Dorud, in the Lorestan province of western Iran, his family witnessed a mob storming the governor's office and setting it on fire. Protesters were fired upon and five people were shot, the source said.

The protests -- described as the largest public display of discontent since the 2009 Green Movement in Iran -- have emerged against a backdrop of rising food and gasoline prices.

In a rare display of public dissent, some protesters directed their ire at Supreme Leader Ayatollah Khamenei, according to some videos on social media. CNN has not independently verified the authenticity of the footage.

"We've seen pictures of (Khamenei) ripped from the billboards at the sides of streets. We've heard protesters call for his overthrow," said Nic Robertson, CNN's international diplomatic editor. "This is something different. This is something the regime is going to take very seriously."

One resident told CNN of witnessing a protester tearing down a poster of Khamenei near Tehran University on Saturday.

Protests in third day

The demonstrations began Thursday in the northeastern city of Mashhad before spreading to other cities. They included Tehran, Kermanshah, Arak, Qazvin, Khorramabad, Karaj and Sabzevar, according to First Vice-President Eshaq Jahangiri, cited by official news agency IRNA.

Iranian media outlets reported a number of arrests.

The unrest has prompted verbal sparring between Iran and the United States, which on Friday urged Tehran to respect protesters' rights and warned that the "world is watching."

An Iranian vice president said on Saturday the government would work harder to resolve economic hardships, according to semi-official news agency FARS.

First Vice President Eshaq Jahangiri made the remarks without acknowledging the protests, adding that some have used economic issues as a "pretext" to hurt the government, FARS reported.

Interior Minister Abdolreza Rahmani Fazli warned that any groups wishing to congregate must file an official request and be granted permission.

"The police and security forces have tried to manage conditions. We have received reports of calls to gather, cyber and social media based, and such calls and any gatherings resulting therefrom, are certainly illegal," he said.

Meanwhile, crowds of government supporters joined official demonstrations held across the country, state media reported.

Angry chants

Protesters have been heard on videos distributed on social media as chanting "Death to Rouhani," a reference to President Hassan Rouhani, who was re-elected earlier this year. CNN cannot independently verify the authenticity of the footage.

In one video circulating on Twitter, throngs of people could be seen gathering close to the university, chanting, "Dishonest! Dishonest!" as a substance that appears to be tear gas is launched through metal gates toward several protesters.

Three students were arrested outside Tehran University on Saturday, an official with the Ministry of Science told semi-official Iran Labor News Agency, ILNA. Two have since been released, it said.

Poorer Iranians have been involved in the new round of protests in a way that wasn't seen in the 2009 Green Movement, an eyewitness in Tehran noted. Iran currently sits 120th on the World Bank's Ease of Doing Business Index, demonstrating the difficult economic situation in the country. The high youth unemployment rate is of particular concern for Iranians.

The pro-government rallies held Saturday were organized in advance to commemorate mass demonstrations held in 2009 to challenge the pro-reform protests.

An eyewitness in Tehran said nearly 2,000 people had gathered peacefully for a pro-government rally. State-run Iranian broadcasters showed demonstrators waving the Iranian flag.

Meanwhile, coverage of the anti-government protests was very limited on state-run media, which referenced them only in passing.

US: 'The world is watching'

The White House voiced its support for anti-government protesters in a statement Friday.

"There are many reports of peaceful protests by Iranian citizens fed up with the regime's corruption and its squandering of the nation's wealth to fund terrorism abroad," said White House press secretary Sarah Sanders. "The Iranian government should respect their people's rights, including their right to express themselves. The world is watching."

President Donald Trump subsequently tweeted the same message.

The US State Department urged the international community to support the Iranian people's "demands for basic rights and an end to corruption."

"Iran's leaders have turned a wealthy country with a rich history and culture into an economically depleted rogue state whose chief exports are violence, bloodshed, and chaos," said spokeswoman Heather Nauert. "As President Trump has said, the longest-suffering victims of Iran's leaders are Iran's own people.

Iranian Foreign Ministry spokesman Bahram Qassemi pushed back against the US comments a day later, saying the Iranian people gave no credence to such "opportunistic" remarks by Trump or his administration.

His statement on the Foreign Ministry website also described "Mr Trump's government" as the main source of ill will toward Iran.

Trump tweeted about the situation again on Saturday, sharing footage of a speech he gave at the United Nations in September.

"Oppressive regimes cannot endure forever," Trump wrote, quoting his speech. "And the day will come when the Iranian people will face a choice."

"The world is watching!" he added.

Relations between Washington and Tehran are tense, with the Trump administration critical of what it sees as Iran's growing regional influence and alleged involvement in conflicts including Yemen and Syria.

Rouhani won a landslide re-election in May after campaigning largely on social reform. His campaign touted the merits of the 2015 nuclear deal with the United States, the European Union and other partners which has been rejected by Trump.

Foreign intervention claim

Iranian officials have pointed to foreign intervention as being behind the anti-government protests.

"Unfortunately, most of the people who participate in these gatherings are unsophisticated individuals who are not aware that these calls for protest are made by anti-revolution elements," Mohsen Hamadani, Tehran deputy governor in charge of security affairs, was quoted as saying by the semi-official news agency ILNA.

"Most participants are not aware that anti-revolution elements are calling people to demonstrate against social issues such as inflation but chant untrue slogans."

Protests stem from 'economic difficulties'

The protests "show that frustration in the Iranian society right now is very extensive, particularly when it comes to the economic difficulties they have been facing," according to Trita Parsi, president of the National Iranian American Council and author of the book "Losing an Enemy."

While the economic situation is due in part to "mismanagement and corruption," Parsi said, it's also a result of the Rouhani government's policies and the process of getting sanctions on the country lifted.

"The nuclear deal is overwhelmingly supported by the Iranian public, but there was an expectation that much more economic development would come out of it," Parsi said. Iranians have not seen that turnaround.

Ultimately, the protests represent an internal dispute within Iran, but international policy is also playing a role, he said. And Trump's involvement is not necessarily beneficial to anti-government protesters.

"This is not about the United States, this is not about Trump," Parsi said. "And Trump stepping into this is not necessarily helpful because he doesn't carry any credibility in Iran."

Parsi pointed to several policy positions taken by the Trump administration this year, such as the administration's opposition to the Iran nuclear deal, his travel ban -- which targeted, in part, Iran -- and his "hugging Saudi Arabia."

"I think he's unaware of how illegitimate broad parts of the Iranian society view him," Parsi said.

While sanctions against Iran were eased under the 2015 deal in exchange for curbs on Tehran's nuclear program, US sanctions imposed over non-nuclear activities continue to have an impact.

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