The rallies took place after Friday prayers as people across the country marched and chanted slogans and held placards in support of the decision.
Demonstrators in Tehran finished the rallies by issuing a statement welcoming the decision and warning the US against any further provocation against the country.
The statement also called for a full suspension of the Joint Comprehensive Plan of Action (JCPOA) if European signatories further failed to uphold the deal.
Iran has complained to Europe for its long-delayed implementation of a promised European financial mechanism designed to bypass US sanctions.
The demonstrations came after Iran’s President Hassan Rouhani announced a decision made by the SNSC on Wednesday.
According to the decision, Iran will stop selling its excess low-enriched uranium and heavy water as it was contractually obliged under the nuclear deal.
Rouhani said Iran would take further steps in 60 days if the other signatories failed again to ensure that it still benefited from staying in the nuclear accord despite the US’s withdrawal.
In a statement, the SNSC has said the order is aimed at “safeguarding the Iranian nation’s security and interests” in the line with national rights under Articles 26 and 36 of the JCPOA.
The document says Tehran has exercised utmost self-restraint and patience since Washington's exit from the deal last May, and has given the remaining signatories “considerable” time at their own request to compensate for Washington’s withdrawal and guarantee Iran’s interests.
Nevertheless, the other parties have failed to adopt any “practical measures” to blunt the impact of the economic sanctions that were re-imposed against Tehran by the US following its withdrawal, the statement said.
The move came after Washington also imposed new sanctions against Iran's enriched uranium exports and metal and mining sectors in the past week.
Last month, the US said it would not renew waivers that allowed Tehran’s eight largest customers to purchase its oil in a bid to cut Iranian oil exports to zero and exert maximum pressure on Iran. The waivers expired on May 1.
Washington withdrew from the Joint Comprehensive Plan of Action (JCPOA) last year and reimposed unilateral sanctions that had been lifted under the deal on Iran.