He also said, "Iran and Russian Federation are facing with common challenges in regional and global fields and we are determined to face them more united than past by drawing a roadmap".
"Our response would be stronger - and swifter - than anything they can imagine", the Iranian president said in comments broadcast live on state television.
"Bilateral, regional and global relations between Iran and Russian Federation have been completely significant in recent years and today, there are very close, friendly relations between the two countries", Iranian President Hassan Rouhani said on Monday after stating that Tehran and Moscow are on the path of strategic relations.
Mr Rouhani dismissed the threat, saying: "It's been 15 months since this gentleman who came to power in America has been making claims and there have been many ups and downs in his remarks and his behaviour".
Rouhani made a speech in Tehran on Monday, amid speculation that President Donald Trump will decide to withdraw from the nuclear agreement as early as May.
"The new US president - who has big claims and many ups and downs in his words and actions - has been trying for 15 months to break the JCPOA (Joint Comprehensive Plan of Action )... but the structure of the JCPOA is so strong that it has not been shaken by such quakes", Rouhani said in a speech broadcast live on state television, according to Reuters.
Rouhani said Iran has been preparing for every possible scenario, including a JCPOA without the United States - which would still include European signatories, China and Russian Federation - or no deal at all.
Rouhani also said Iran will launch new facilities in the Fordow enrichment establishments in central Iran.
On Sunday, Ali Akbar Salehi, the head of Iran's Atomic Energy Organization, told that state-run press that Iran has the power to begin enriching uranium - needed to create nuclear weapons - to 20% within just four days of the Supreme Leader Ali Khamenei giving the order.
Seven Iranian military personnel were killed in Sunday's air strike on a Syrian air base, Tasnim news agency said, nearly double the number originally reported.