"I heard news that Mr Mojtaba Khamenei had been injured. I have asked some friends who had connections," Yousef Pezeshkian, who is also a government adviser, wrote in a post on his Telegram channel.

"They told me that, thank God, he is safe and sound," added the son of President Masoud Pezeshkian.

Mojtaba Khamenei, until now a low profile if powerful behind-the-scenes figure, was named Iran's number one following the killing of his father Ali Khamenei in an air strike at the start of the US-Israeli war against the Islamic republic.

But there had been mounting questions about his whereabouts and physical condition after his appointment by the Assembly of Experts clerical body, with the new supreme leader yet to be seen, let alone speak, in public.

State television had called Khamenei a "wounded veteran of the Ramadan war" without giving details, in reference to the conflict which broke out during the holy Muslim fasting month.

In a report on Wednesday, the New York Times quoting three unnamed Iranian officials said that Khamenei "had suffered injuries, including to his legs, but that he was alert and sheltering at a highly secure location with limited communication".

There has been speculation that he was injured in the day-time air strike on a compound in Tehran that killed his father, as well as his mother and wife on the first day of the war on February 28.

His face has appeared on giant billboards in Tehran, with one showing him symbolically receiving the national flag from his father Ali while the founding leader of the Islamic republic, Ruhollah Khomeini, looks on.

Posters of him were brandished by thousands of pro-government supporters at a huge rally in central Tehran on Monday.

But night-time cries of "Death to Mojtaba!" in the capital have also underlined public opposition to a figure believed to have played a key role in repressing waves of anti-government protests since 2009.

Mojtaba's father Ali lived the latter half of his life with a partially paralysed arm, having been injured in an assassination attempt in 1981 blamed on the People's Mujahedin of Iran (MEK) group.

The Iranian supreme leader position is for life and he also serves as a religious guide for Shia Muslims.

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Given that he instantly became a target for assassination by the United States and Israel at the weekend, analysts said he would remain out of public view for some time.

Emile Hokayem at the London-based International Institute for Strategic Studies said he expected him "to sit in a bunker somewhere for a very long time because he saw what happened to his father, his wife, his mother who were all killed in the initial attack."

"Killing him early is certainly an Israeli priority. If he survives, he becomes a totem, a testimony to the resilience of the system," Hokayem told an online event organised by his think-tank on Monday.

He said he expected Khamenei to delegate power to run the government to national security chief Ali Larijani and the war effort to powerful parliament speaker Mohammad Bagher Ghalibaf.

The army and the powerful Islamic Revolutionary Guard Corps (IRGC) both pledged allegiance to Khamenei after his nomination, as did the Tehran-backed Houthi rebels in Yemen and the Hezbollah armed group in Lebanon.

Russian President Vladimir Putin promised "unwavering support".

Before his nomination to the position, US President Donald Trump had warned that Khamenei would be "unacceptable" as new supreme leader.

"He's going to have to get approval from us," Trump told ABC News on Sunday. "If he doesn't get approval from us he's not going to last long."

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