The law came as a response to Iran’s pick of Hamid Aboutalebi as UN envoy.
Hamid Aboutalebi was linked to the student militants who overran the US embassy in Tehran in 1979.
The US has already denied Hamid Aboutalebi a visa, and Barack Obama said he would treat the new law as “advisory”.
Iran has lodged a formal complaint with the UN over the rejection.
The bill that Barack Obama signed into law on Friday passed both houses of Congress handily following uproar over Hamid Aboutalebi’s links to the students who seized the US embassy in Tehran in 1979 and held the American diplomats hostage.
Hamid Aboutalebi has said that he acted merely as a translator on a couple of occasions for the hostage-takers, an account corroborated by some of the activists.
A senior political adviser to President Hassan Rouhani, he has previously served as the Iranian ambassador to Italy, Belgium and Australia.
In a statement on Friday upon signing the bill, Barack Obama said: “I share the Congress’ concern that individuals who have engaged in such activity may use the cover of diplomacy to gain access to our nation.”
However, Barack Obama said the law could effectively curtail his power under the US constitution to receive or reject ambassadors, and thus he said he would treat the law “as advisory in circumstances in which it would interfere with the exercise of this discretion”.
Under the 1947 Headquarters Agreement, the US is generally required to grant visas to persons invited to the UN in New York.
Iran’s deputy envoy at the UN, Hossein Dehghani, has asked Committee on Relations with the Host Country for a meeting over the decision, saying the US had violated its legal obligations under international law.
“This decision of the US government has indeed negative implications for multilateral diplomacy and will create a dangerous precedence and affect adversely the work of intergovernmental organizations and activities of their member states,” Hossein Dehghani warned.
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