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".
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.
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.
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