Opposition inside Iran to the interim nuclear agreement between the administration of Hassan Rouhani and six world powers has gathered strength after the Iranian president labelled his domestic critics "a bunch of uneducated people".

As hundreds of thousands of Iranians rallied across the country to mark the 35th anniversary of the Islamic revolution on Tuesday, Rouhani's critics distributed leaflets asking whether his government had made too many concessions in the Geneva negotiations last year.

"Did you know that all sanctions imposed by the UN security council, the European Union and the US will remain in place despite the agreement?" reads one of the leaflets. It makes several claims that are untrue, including that economic sanctions and oil embargo will not be lifted even if Iran settles its nuclear dispute with the west.

Another asks: "In the final stage of the negotiations, did you know that only nuclear-related sanctions will be removed and not main punitive measures such as banking and oil sanctions?"

Last week Rouhani urged university professors and elites to publicly support his diplomacy.

"Why is the university silent? Why are the professors silent? What are you afraid of?" the president said, according to quotes carried by the conservative YJC news agency. "Why should only a small number of people talk? Why must there be a bunch of uneducated people doing all the talk while our university professors talk in private? Why don't you step forward? The future will not forgive us for this."

The fiery speech was met with criticism among Rouhani's own supporters, some of whom said the language was inappropriate and echoed that of his predecessor, Mahmoud Ahmadinejad.

The semi-official Isna news agency reported that a statement issued by "the people's movement for defending Iran's independence" alleged there was a secret agreement between Iran's foreign ministry and the US and EU. Rouhani's government has vehemently denied claims about a secret agreement parallel to the interim deal.

It was not immediately clear which political group in Iran was behind the leaflets, but much of the criticism of Rouhani's nuclear diplomacy in recent months has come from supporters of the former nuclear negotiator Saeed Jalili. Jalili, a hardliner who negotiated with the west under Ahmadinejad, ran against Rouhani in last year's presidential elections but performed poorly.

As part of the Geneva deal, Tehran agreed to roll back its nuclear programme and accept more scrutiny of its activities, in exchange for partial relief from sanctions. Last month both sides made the first step in implementing the interim deal, with Iranian scientists halting all enrichment of uranium to 20% concentration.

In return, the EU eased restrictions on trade in petrochemicals, precious metals and on the provision of insurance for oil shipments. The US treasury released $550m (£335m) to Iran, the first instalment in $4.2bn of frozen oil revenues that the Islamic republic is expected to receive as part of the deal.

Conservatives who have dominated the Iranian parliament have voiced opposition to the agreement and criticised the government for not involving them directly in the negotiations. But an apparent blessing for the six-month agreement from the supreme leader, Ayatollah Ali Khamenei, who has the final say on all state matters, has limited their room to attack Rouhani.

In a speech aired live on national television last week, Rouhani defended the interim agreement once more, prompting some MPs to ask the broadcaster to give them airtime to respond.

A number of placards carried by people in Tuesday's demonstrations displayed similar messages to those of the leaflets. "We promise to open our eyes in the next elections," read one, according to images posted on Twitter. "Centrifuges spin no more, but for what price? A basket of food?" read another, referring to Rouhani's initiative for distribution of food rations among people.

"We uneducated people who have obtained our nuclear energy by sacrificing our blood will not change it with a piece of bread," said another placard. "I'm uneducated but I will not accept tyranny."

Some participants in the rallies also shouted "death to America" and set fire to the US and union flags, local agencies said. Some carried placards reading "we are eager for the options on the table", referring to comments made by US officials in the past that all options were on the table about the future of Iran's nuclear activities.

Rouhani has stood firm over the agreement so far. In his speech, he said: "I say explicitly to those delusional people who say the military option is on the table, that they should change their glasses … Our nation regards the language of threat as rude and offensive."

He added: "I want to expressly announce that the movement of the Iranian nation towards the peaks of scientific and technical progress and advancement, including peaceful nuclear technology, will be forever."

The next round of talks between Iran and Britain, France, Germany, China, Russia and the US – the group known as P5+1 – over a comprehensive accord is scheduled for 18 February in Vienna.