"I am not an expert and there are different opinions but I had said that if the heads of the three branches make a decision I will support it", he said in a speech aired on state television.
The protests flared hours after it was announced that the price of petrol would be raised by 50 percent for the first 60 litres (16 gallons) and by 300 percent for anything above that each month.
"People have the right to protest".
But journalists in Iran and worldwide news agencies report the situation is much worse, citing clashes between protesters and riot police, damage to public property, and tires and garbage burning on the ground.
Sirjan's acting Governor Mohammad Mahmoudabadi also told journalists that some violent elements within a largely "calm gathering" damaged public property, including fuel stations, sought access to a local oil company's major fuel depots and even set them on fire.
An Iranian policeman died Sunday after being shot in a clash with "rioters and thugs" during protests against petrol price hikes, state news agency IRNA reported.
The gasoline pricing plan was agreed by the High Council of Economic Coordination made up of the president, parliament speaker and judiciary chief.
After two days of intermittent government slowdown of the internet amid widespread protests in Iran, internet services were nearly completely stopped Saturday evening, plunging the country into cyber darkness.
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"Some people would definitely get upset over this decision ... but damaging and setting fire (to property) is not something (normal) people would do".
Iran's Intelligence Ministry said protest leaders had been identified.
Access to the internet has been restricted since the demonstrations broke out.
The administration of U.S. President Donald Trump, which has dropped out of an worldwide nuclear deal with Iran and reinstated economic sanctions, expressed support for what it called "peaceful protests against the regime".
The U.S. State Department immediately condemned "the attempted shutdown of the internet" in a tweet on November 17, calling on the Iranian government to "Let them speak".
Khamenei's remarks came a day after nationwide protests erupted in dozens of cities, including Tehran, to reject a decision on Friday by the government of President Hassan Rouhani to impose the new measures.
Many shops in Tehran's bazaar closed today, after "disruptions" by people from outside the trading centre, ISNA reported, Businesses were expected to re-open after police reinforcements arrived, it said.
One firm said it was the biggest internet outage ever seen in Iran.