Iran's judiciary has denied it scheduled the execution of a man arrested in connection with the country's recent protests.

Norway-based Kurdish human rights organisation Hengaw said earlier this week that the family of Erfan Soltani, 26, had been told he faced execution on Wednesday, only days after he was detained.

On Wednesday, Hengaw cited them as saying Soltani's execution had been "postponed" but warned that "serious and ongoing concerns" regarding his life remained.

"This is good news. Hopefully, it will continue!" said US President Donald Trump, who had warned Iran not to execute protesters.

The judiciary said he faced charges of "colluding against national security" and "propaganda activities against the establishment", which are not punishable by the death penalty, state broadcaster IRIB reported.

They said reports by foreign media organisations that Soltani faced execution was a "blatant act of news fabrication".

Iranian Foreign Minister Abbas Araghchi also said there was "no plan" to hang people.

It came after President Trump threatened to take "very strong action" if executions were carried out, amid mounting speculation of possible US military strikes.

On Wednesday, he told reporters that "very important sources on the other side" had informed him "the killing in Iran is stopping, and there's no plan for executions".

Hengaw told the BBC that Soltani had been denied access to a lawyer and that his family were unaware of any official charges brought against him.

Soltani, a clothes shop owner, was arrested at his home last Thursday in connection with the protests in the northern city of Fardis, west of Tehran, according to the group and his family.

However, the judiciary said he was arrested during "riots" on Saturday and was being held in a prison in the neighbouring city of Karaj.

Iran's chief justice, Gholam-Hossein Mohseni-Ejei, has advocated for the swift trial and punishment of arrested "rioters".

"Those elements who beheaded people in the streets or burned people alive must be tried and punished as quickly as possible," he said in a video on Wednesday. "If we don't do it fast, it won't have the same impact."

The current wave of protests began after shopkeepers in Tehran went on strike over the rising cost of living and the depreciating value of the currency.

They quickly spread across the country and turned against Iran's clerical establishment, particularly the Supreme Leader, Ayatollah Ali Khamenei. The slogans chanted by demonstrators have included "Death to the dictator" and "Seyyed Ali [Khamenei] will be toppled this year".

The protests escalated significantly last Thursday and were met with deadly force by authorities, masked by a near total shutdown of the internet and communication services.

According to the US-based Human Rights Activists News Agency (HRANA), at least 2,435 protesters have been killed since the unrest began, as well as 13 children and 153 people affiliated with the security forces or government.

It reports that another 18,470 protesters have been arrested.