Iran's president came under fire from MPs Tuesday for branding his critics as "political cowards' and urging them "go to hell" if they insist on opposing his policies.

President Hassan Rouhani's remarks 24 hours earlier were aimed at hardline conservatives who have bridled at his efforts to improve relations with the West and secure a nuclear deal.

But denouncing his opponents prompted a backlash from dozens of MPs who signed a letter demanding that Rouhani come to parliament to explain himself.

One conservative lawmaker said that 200 of the parliament's 270 members would eventually sign the letter.

According to another MP quoted on Iranian media, parliament speaker Ali Larijani told a closed meeting that Rouhani's words were "indefensible and unacceptable".

But Larijani went on to urge lawmakers "not to make a big deal of it because the country's economic problems are significant" and more worthy of their attention.

In his fiery speech, Rouhani attacked the hardline factions within parliament who have consistently opposed him, particularly on the nuclear issue, since he took office after a surprise electoral victory last year.

"Some of them chant slogans but they are political cowards," he said of those who are sceptical or against a nuclear agreement.

"As soon as we negotiate they start shaking. Go to hell and find somewhere to stay warm," Rouhani told his opponents.

A moderate whose tenure has so far focused on economic and foreign policy, Rouhani said Iran faces three phobias abroad: Iranophobia, Islamaphobia and Shiaphobia.

But on the home front, the country must confront "Ententephobia" from those who oppose his overtures to the rest of the world for better relations after years in the diplomatic wilderness.