President Hassan Rouhani said on Monday Iran's position in the Middle East had never been stronger but that the regime was at risk unless infighting between political factions was curbed.

"The greatness of the nation of Iran in the region is more than at any other time," Rouhani said in a speech in Tehran, carried by the state broadcaster.

"In Iraq, Syria, Lebanon, northern Africa, in the Persian Gulf region -- where can action be taken without Iran?"

Rouhani did not directly respond to comments on Sunday by US Secretary of State Rex Tillerson, who called on Iran-backed militias fighting jihadists in Iraq to "go home".

But despite its powerful position in the region, Rouhani said Iran's regime was under threat from fierce infighting between conservatives and moderates at home.

"We should not think that damaging one part of the system will strengthen the other part. No, the whole system will collapse," he said.

There has been renewed criticism from hardliners over the nuclear deal Rouhani's administration signed with world powers.

On Sunday, state television read out in its entirety a letter by supreme leader Ayatollah Ali Khamenei from 2015 in which he warned against trusting the United States and other signatories to the deal.

Although the accord was explicitly endorsed by the supreme leader, hardliners have consistently lambasted Rouhani for going too far in his efforts to rebuild ties with the West.

Those criticisms have become more pointed in recent days as US President Donald Trump has thrown the nuclear deal's future into doubt, calling for renewed sanctions to rein in Iran's build-up of influence, particularly in Iraq and Syria.

But Rouhani said his US counterpart was failing in his efforts to undermine the deal.

"Every day (Trump) says this agreement is the worst deal in history. As he put it, it is shameful for America. But still he hasn't been able to do anything with this agreement," Rouhani said.