Former US President Donald Trump withdrew Washington from the landmark nuclear deal in 2018 but Joe Biden has indicated that the U.S. would be willing to rejoin.
State TV reported the country had officially begun restrictions on nuclear inspections, in what is seen as a bid to pressure the west into lifting sanctions and restore the 2015 nuclear deal.
There are fears of a renewed US-Iran clash a year after the US drone killing of the Revolutionary Guard chief, in the dying days of Donald Trump's presidency.
Iran executed a once-exiled journalist over his online work that helped inspire nationwide economic protests in 2017.
The bill would suspend U.N. inspections and require the government to resume enriching uranium to 20% if European nations fail to provide relief from crippling U.S. sanctions on the country's oil and banking sectors.
"The execution of Iranian wrestler Navid Afkari is very sad news," the International Olympic Committee said.