Iran's supreme leader has blamed the US and Israel for the protests sweeping the country following the death of a woman whilst in police custody.

In his first public comments on the unrest, Ayatollah Ali Khamenei said "riots" had been "engineered" by Iran's arch-enemies and their allies.

The protests are the biggest challenge to his rule for a decade, and he urged security forces to be ready for more.

The US said it was "appalled" by the violent response to the protests.

President Joe Biden said he was "gravely concerned" about reports of the "intensifying violent crackdown on peaceful protesters".

Those protesters were calling for "just and universal principles", he said, adding that the US "stands with Iranian women" who were "inspiring the world with their bravery".

The UK echoed the sentiment, summoning Iran's most senior diplomat in London to tell their leaders in Tehran that "instead of blaming external actors for the unrest, they should take responsibility for their actions and listen to the concerns of their people".

Mahsa Amini, a 22-year-old Kurdish woman, fell into a coma hours after being detained by morality police on 13 September in Tehran for allegedly breaking the strict law requiring women to cover their hair with a hijab, or headscarf. She died three days later.

Her family has alleged that officers beat her head with a baton and banged her head against one of their vehicles. The police have said there is no evidence of any mistreatment and that she suffered "sudden heart failure".

Women have led the protests that began after Ms Amini's funeral, waving their headscarves in the air or setting them on fire to chants of "Woman, life, freedom" and "Death to the dictator" - a reference to Ayatollah Khamenei.

Addressing a graduation ceremony of police and armed forces cadets on Monday, the supreme leader said Ms Amini's death "broke our hearts".

"But what is not normal is that some people, without proof or an investigation, have made the streets dangerous, burned the Quran, removed hijabs from veiled women and set fire to mosques and cars," he added, without mentioning any specific incidents.

The ayatollah, who has the final say on all state matters, asserted that foreign powers had planned "rioting" because they could not tolerate Iran "attaining strength in all spheres".

"I say clearly that these riots and the insecurity were engineered by America and the occupying, false Zionist regime [Israel], as well as their paid agents, with the help of some traitorous Iranians abroad."

The supreme leader often blames protests and other internal issues on meddling by Iran's foreign enemies, and he provided no evidence to support his claim.

He also gave his full backing to the security forces, saying that they had faced "injustice" during the unrest.

Iran Human Rights, a Norway-based group, has said at least 133 people have been killed by security forces so far. State media have reported that more than 40 people have died, including security personnel.

The US has already imposed sanctions on Iran's morality police, and President Biden said that this week his administration would "impose further costs" on those perpetrating violence against peaceful protesters.

Ayatollah Khamenei's comments came a day after security forces violently cracked down on a protest by students at Iran's most prestigious science and engineering university, reportedly arresting dozens.

The BBC's Kasra Naji says security forces tried to enter the campus of Sharif University of Technology in Tehran on Sunday night, but the students drove them back and closed the gates.

But, our correspondent adds, a siege developed and the students who tried to leave through a car park were picked up one by one and beaten, blindfolded and taken away.

On Monday, students at the university announced they would not go back to classes until their fellow students had been released.

Protests were also reported at other universities in Tehran and elsewhere in the country.

Schoolgirls were also filmed waving their headscarves in the air and chanting "death to the dictator".