Videos posted on social media on Saturday showed two young Iranian men lying motionless on the ground and covered with blood and a voiceover said they had been shot dead by police.
It said security forces fired on protesters in the western town of Dorud and killed at least two.
A witness claimed he saw a mob storming the governor’s office and setting it on fire before protesters were fired upon and five people shot.
Other protesters in the same video were chanting, “I will kill whoever killed my brother!”
The Secretary of the National Council of Resistance of Iran said: “This inhuman crime occurred while the suppressive forces failed to disperse protesters by tear gas and beating them.
“The details and the names of the martyrs will be announced later.
“Without a doubt, this unjust bloodletting will double the anger of the people against the clerical regime, further inflame the fire of uprising, and accelerates its overthrow.
“The Iranian Resistance calls on the United Nations Security Council, the European Union, the United States and all human rights organisations to condemn this great crime and to take efficient international measures to confront the suppression of the uprising of the Iranian people.”
The violence comes on the third day of protests, the largest public display of discontent since the 2009 Green Movement in Iran.
Demonstrations began on Thursday in Mashhad before spreading to cities across the nation on Friday, including to Tehran.
State television showed a rally in the capital Tehran as well as marchers carrying banners in support of Supreme Leader Ayatollah Ali Khamenei in Mashhad, Iran’s second largest city where protests over prices turned political on Thursday.
State-sponsored mass rallies were scheduled in more than 1,200 cities and towns, state TV said – events held annually to commemorate the end of months of street protests that followed Mahmoud Ahmadinejad’s disputed re-election as president.
At the same time, social media postings said protests broke out for the third straight day in cities including Tehran and Kermanshah.
One video showed dozens of protesters booing after police announced by loudspeaker that any gathering would be illegal.
The semi-official news agency Fars said up to 70 students gathered in front of Tehran University and hurled rocks at police.
A social media video showed them chanting “Death to the dictator”, an apparent reference to Khamenei.
Footage later showed riot police clubbing and arresting the protesters.
ISNA news agency said a group of government supporters also gathered outside the university as police tried to disperse protesters.
Authorities closed two nearby metro stations “until the end of the unrest”, ISNA said.
Another video appeared to show security forces arresting demonstrators in another part of Tehran, with protesters shouting “Let him go! Let him go!”
In a further video, which could not be verified, marchers in the western town of Dorud chanted, “Death to the dictator”.
Dozens of protesters gathered in the western city of Shahr-e Kord, ISNA said. Social media footage appeared to show a protester being helped by his comrades after being teargassed.