The two were reported killed overnight at a demonstration in Dorud, in the country’s western Lorestan province.
They are the first deaths to be reported since the current wave of protests erupted on Thursday and spread across Iran.
The province’s governor, Habibollah Khojastehpour, told state television: “On Saturday evening, there was an illegal protest in Dorud and a number of people took to the streets responding to calls from hostile groups, leading to clashes.
“Unfortunately in these clashes two citizens from Dorud were killed.”
He said “no shots were fired by the police and security forces”, and blamed “foreign agents” and “enemies of the revolutions”.
Videos appearing to show the bloodied bodies of those said to have been killed has been widely shared on social media, but there has been no independent verification of footage.
A Revolutionary Guards Telegram channel said the deaths had been caused by “people armed with hunting and military weapons” who “entered the protests and started shooting randomly toward the crowd and the governor’s building”.
The channel also said six people were wounded.
The mass unrest spreading across the country has led to the biggest political demonstrations in the country in nearly a decade. The protests were prompted by discontent over the country’s weak economy and alleged corruption.
Speaking on state television early on Sunday, Iranian interior minister Abdolrahman Rahmani Fazli warned protesters.
“Those who damage public property, disrupt order and break the law must be responsible for their behaviour and pay the price,” he said.
On Saturday, US President Donald Trump released a series of tweets, warning Tehran to respect freedom of speech.
“The entire world understands that the good people of Iran want change, and, other than the vast military power of the United States, that Iran’s people are what their leaders fear the most,” he wrote.
“Oppressive regimes cannot endure forever, and the day will come when the Iranian people will face a choice. The world is watching!”
Many reports of peaceful protests by Iranian citizens fed up with regime’s corruption & its squandering of the nation’s wealth to fund terrorism abroad. Iranian govt should respect their people’s rights, including right to express themselves. The world is watching! #IranProtests
— Donald J. Trump (@realDonaldTrump) December 30, 2017
The protests originally began in Mashhad, Iran’s second-largest city, when hundreds of people took to the streets to protest against high prices.
The unrest then spread to Tehran, and quickly turned against the Islamic regime as a whole.
Police used water cannon in some cases to disperse the crowds and arrested 52 people.
On Saturday, tens of thousands of government supporters marched in cities across Iran in a show of support for the regime.
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Many of the marchers carried banners backing Supreme Leader Ayatollah Ali Khamenei.
In 2009, Iran saw eight months of civil unrest when tens of thousands of people took to the streets to protest Iran’s disputed 2009 presidential election.