Tensions between Tehran and Washington have risen in recent months.
The US tightened economic sanctions against Iran following its withdrawal from the 2015 nuclear deal in May 2018, ordering all countries and companies to halt all imports of Iranian oil or be banished from the global financial system.
It has also recently deployed an aircraft carrier and other extra hardware to the Middle East to counter what it calls a threat from Iran.
"I am worried about increasing tensions over the Iranian nuclear issue," International Atomic Energy Agency chief Yukiya Amano said in a speech to a meeting of the IAEA's 35-nation Board of Governors, one of its main decision-making bodies.
On the first anniversary of the US withdrawal from the nuclear deal, Iran announced that it would suspend the implementation of some of its commitments under the deal, adding that it would stop exporting excess uranium and heavy water, setting a 60-day deadline for the remaining parties to the deal to take practical measures towards ensuring its interests in the face of the American sanctions.
In its quarterly report on May 31, the IAEA said Iran's increased stocks of key nuclear materials are still within the limits set by the nuclear deal, officially known as the Joint Comprehensive Plan of Action (JCPOA).
Amano said on Monday that Iran has followed through on its threat to accelerate its production of enriched uranium.
"As I have constantly emphasized, the nuclear-related commitments entered into by Iran under the JCPOA represent a significant gain for nuclear verification," he said.
"It is essential that Iran fully implements its nuclear-related commitments under the JCPOA," he added.
Iran and the five permanent members of the United Nations Security Council – the United States, France, Britain, Russia and China – plus Germany signed the nuclear agreement on July 14, 2015 and started implementing it on January 16, 2016.
Under the JCPOA, Iran undertook to put limits on its nuclear program in exchange for the removal of nuclear-related sanctions imposed against Tehran.
However, US President Donald Trump pulled his country out of the JCPOA in 2018 and reimposed harsh sanctions against the Islamic Republic in defiance of global criticisms.
Reuters and AFP contributed to this story.