"We have grounded five Airbuses out of 16 because we are unable to purchase the engines," said Malek Barzegar-Sedigh, Iran Air spokesman on Tuesday.
Airbus engines are US-made.
He accused Washington of putting passenger safety at risk.
"The country which boasts more than any other country about human rights endangers many invaluable lives by resorting to such political measures." Barzegar-Sedigh said.
Washington agreed in March to ease its tough sanctions and allow some civilian aircraft spare parts sales to the Islamic state, in support of a European Union package of incentives aimed at persuading Tehran to abandon its atomic programme.
But the EU talks with Iran have broken down and there have been no reports of aircraft spare parts being sold to Iran under this case-by-case waiver.
Unable to buy new aircraft or spare parts from the West, Iran has supplemented its fleet of Boeing and Airbus planes with aircraft from former Soviet Union countries.
Iran has a poor airline safety record, according to air safety experts.
Some foreign companies operating in Iran discourage their employees from taking certain types of aircraft on internal routes or using Iran Air for international flights.
Barzegar-Sedigh said Iran Air had formed a counter-sanctions committee charged with finding ways to get around the sanctions and obtain spare parts.
US sanctions on Iran do allow for the sale of spare parts related to the safety of civilian aircraft, but only if the aircraft themselves are of US origin.
At the same time, they bar the export of any US spare parts to Iran that would constitute more than 10% of the value of the finished product.