Mr Trump earlier this year pulled the United States out of the global deal meant to prevent Tehran from developing a nuclear weapon and ordered increased American sanctions, as well as threatening penalties for companies from other countries that continue to do business with Iran.
"We'll see what happens, but we're ready to make a real deal, not the deal that was done by the previous administration, which was a disaster", he said during a speech to the Veterans of Foreign Wars.
Most Republicans have stayed silent on Iran following Trump's all-caps tweet warning the terrorist nation against threatening the US again, but Graham came out in support of Trump for taking a tough stance.
Iranian Supreme Leader Ayatollah Ali Khamenei on Saturday supported Rouhani's suggestion of blocking oil shipments through the Persian Gulf if Iran is prevented from selling its oil by US sanctions which come into effect in November. Still, there has been little tangible progress in a global push to rid North Korea of its nuclear weapons program since the historic Trump-Kim Jong Un summit on June 12.
US President Donald Trump is unlikely to get the boot from Twitter even after threatening Iran with dire consequences as the microblogging site sees the world leaders with a different lens. "Obama will someday attack Iran in order to show how tough he is".
Mr Rouhani also said: "We should respond to them with action".
He worries about the influence of an Iranian exile group that advocates the overthrow of the Iranian government and was included on the US terrorist list until 2012. "President Putin is very much involved now with us in a discussion with Bibi Netanyahu on working something out with surrounding Syria and - Syria, and specifically with regards to the security and long-term security of Israel", Trump said last week.
In his tweet to Rouhani, Trump had threatened "CONSEQUENCES THE LIKES OF WHICH FEW THROUGHOUT HISTORY HAVE EVER SUFFERED BEFORE" if Iran continued to threaten the United States. He's author of the book, The Iranian Constitutional Revolution and the Clerical Leadership of Khurasani. And Saudi Arabia, whose leaders have worked to build a cozy relationship with Trump, has been after Trump to curb Iran's influence in the region.
But Ghaemi, speaking via Skype, said the Trump administration's other policies hurt average Iranians. Iran has insisted it will not renegotiate the deal.