The report by the IRAN daily quoted Interior Minister Abdolreza Rahmani Fazli as saying Iranian border guards stopped several travellers en route to Iraq and had "three cases of arrests."
Fazli, who spoke at a meeting of provincial governors along with Iran's chief of police, said that Afghan and Pakistani nationals were arrested but did not provide a breakdown.
The report did not say when or where the arrests happened. Fazli's remarks were a rare mention by an Iranian official of the possibility of Islamic State supporters being present in Iran.
Tehran also provides military advisers to Baghdad in the anti-militant campaign against the mostly Sunni militants. It denies having any forces on the ground in neighbouring Iraq. President Barack Obama is seeking an international coalition to challenge the Islamic State group and is expected to outline his plan tomorrow.
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The US began conducting airstrikes last month against Islamic State fighters in Iraq in what amounts to the first American militarily action in the country since American troops left in 2011.
The report also quoted the police chief, Gen. Ismail Ahmadi Moghadam, as saying that there have been reports, apparently from Iranian Sunni families, that the Islamic State group has tried to recruit their sons.
He assured the audience that "there is no room for concern," adding that Iran's police is "fully ready" to face any threats from the militant group.