"The Islamic Republic of Iran will always stick to its international commitments," Rouhani said in a televised cabinet meeting.

But if the US wants "to press forward with new sanctions under any pretext... the great nation of Iran will respond appropriately," he said.

"We will not forgive violations by the Americans and we will stand against them."

His comments came a day after the US and Iran traded tit-for-tat sanctions over the Islamic republic's ballistic missile programme.

The State Department slapped sanctions on 18 individuals and entities in Iran, hours after the White House admitted Tehran was adhering to the 2015 agreement.     Iran hit back with its own sanctions against "American people and entities that have acted against the Iranian people and other Muslim peoples of the region."

Rouhani on Wednesday accused Washington of "duplicity".