Following the Iranian authorities' deadly response to anti-government protests that peaked last month, Trump has threatened military action and ordered the dispatch of an aircraft carrier group to the Middle East.

While piling pressure on Iran, Trump has maintained he is hopeful of making a deal and Tehran has also insisted it wants diplomacy while vowing an unbridled response to any aggression.

"President Pezeshkian has ordered the opening of talks with the United States," the news agency Fars reported on Monday, citing an unnamed government source.

"Iran and the United States will hold talks on the nuclear file," Fars said, without specifying a date. The report was also carried by the government newspaper Iran and the reformist daily Shargh.

Iran said earlier Monday it was working on a method and framework for negotiations that would be ready in the coming days, with messages between the two sides relayed through regional players.

"Several points have been addressed and we are examining and finalising the details of each stage in the diplomatic process, which we hope to conclude in the coming days," foreign ministry spokesman Esmaeil Baqaei said, without giving details on the content of any negotiations.

Trump had warned "time is running out" for Iran to reach a deal on its nuclear programme, which the West believes is aimed at making an atomic bomb.

But Baqaei said Tehran "never accepts ultimatums" and that he could not confirm any such message was received.

Regional players have pushed for diplomacy to defuse tensions.

Iranian Foreign Minister Abbas Araghchi was in Turkey last week and held further calls with his Egyptian, Saudi and Turkish counterparts, he said on Telegram.

"President Trump said no nuclear weapons, and we fully agree. We fully agree with that. That could be a very good deal," Araghchi told CNN on Sunday.

"Of course, in return, we expect sanctions lifting. So, that deal is possible. Let's do not talk about impossible things."

Baqaei said the rallying of neighbouring states around a diplomatic solution demonstrated a fear any US attack would drag the region into conflict, echoing Iranian supreme leader Ayatollah Ali Khamenei, who warned on Sunday a US attack would trigger a "regional war".

- Ambassadors summoned -

The supreme leader also likened the recent protests to a "coup" attempt.

Authorities have said the protests, which were sparked by economic strain and exploded in size and intensity over several days in early January, were "riots" inflamed by its arch foes the United States and Israel.

Tehran has acknowledged thousands of deaths during the protests, and on Sunday the presidency published the names of 2,986 people out of the 3,117 whom authorities said were killed in the unrest.

Authorities insist most were members of the security forces and innocent bystanders, attributing the violence to "terrorist acts".

US-based Human Rights Activists News Agency said it has confirmed 6,842 deaths, mostly protesters killed by security forces, with rights groups warning the figure is likely far higher.

The crackdown prompted the European Union to list the Islamic Revolutionary Guard Corps (IRGC) as a terrorist organisation, with Iranian lawmakers retaliating on Sunday by slapping the same designation on European armies.

Baqaei said Monday the foreign ministry had summoned all the EU member state ambassadors in Tehran over the designation, and that other responses were to come.

Iranian state television also announced four foreigners had been arrested in Tehran for "participation in riots", without specifying their nationalities.

Authorities have continued to announce arrests, with rights groups estimating at least 40,000 people have been detained over the protests.

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