The ISNA news agency reported Deputy Foreign Minister Abbas Araghchi as saying Tehran had consulted with European countries on countering the new law passed by Congress on Friday.
"This law certainly affects economic, tourist, scientific and cultural exchanges with Iran and it contravenes the nuclear deal," Araghchi said.
The US measure bars citizens of the 38 countries that participate in the Visa Waiver Program (VWP) and who are also dual nationals from Iran, Iraq, Syria and Sudan from using the visa-free system.
It also prevents those who have travelled to those four countries since 2011, or to a country Washington has listed as supporting terrorism, from participating, deeming them a risk and requiring them to apply for a standard visa.
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The measure formed part of a sprawling bill that funds the US government until next September.
European diplomats, led by European Union ambassador to Washington David O'Sullivan, have warned of potential retaliation against the United States, arguing that the programme is based on reciprocity.
"If this law is applied, we will put forward a request to the Joint Commission, because the law goes against the nuclear accord," Araghchi said.
In July, Iran and the five permanent UN Security Council members -- Britain, China, France, Russia and the United States -- plus Germany reached a landmark accord on curb Tehran's nuclear programme in return for a lifting of sanctions.
The Joint Commission oversees implementation of the accord.