The UK wants to see a “peaceful transition” of power in Iran, a cabinet minister has said, after Donald Trump said he could support protesters with military force.

As the US weighs the option of military strikes, Heidi Alexander, the transport secretary, said she would not be drawn on America’s foreign policy towards Iran, where protests have been met with a violent police response.

She told Sky News Iran was a hostile state posing a security threat in the Middle East and repressing its own people, so the “priority, as of today, is to try and stem the violence that is happening in Iran at the moment”.

Kemi Badenoch, the Conservative leader, went further in saying she would “not have an issue” with seeing the Iranian regime removed and that it could be right for the US and its allies to be involved in that process.

She told the BBC’s Sunday With Laura Kuenssberg programme: “Iran would very happily wipe out the UK if it felt it could get away with it. It has tried to kill people on our soil. It is an enemy, it calls us the little Satan.

“So, no, I don’t have an issue with removing a regime that is trying to harm us. It has its terrorist outposts with Hezbollah all across the world.

“But what I want us to do is try and find a way to make sure as a country we are strong, we protect ourselves from threats and reduce the escalation of what I see around the world, an increasing escalation of conflict everywhere.”

Asked if it would be right for the US and its allies to be involved in regime change, Badenoch added: “Given the threat that we’re seeing to the people, I think that would be right.”

In the US, Trump has threatened repeatedly to intervene if Iranian authorities killed protesters. He said on Friday that the Iranian authorities were “in big trouble”, adding: “You better not start shooting, because we’ll start shooting too.”

On Saturday night, Trump said the US was “ready to help” as protesters in Iran faced an intensifying crackdown by authorities of the Islamic republic.

“Iran is looking at FREEDOM, perhaps like never before. The USA stands ready to help!!!” Trump said in a social post on Truth Social.

Earlier this week, Keir Starmer condemned the killing of protesters in the country and urged Tehran to “exercise restraint” amid a crackdown on demonstrations against the regime.

A UK government spokesperson said: “We are deeply concerned by reports of violence against protesters in Iran who are exercising their legitimate right to peaceful protest and are monitoring the situation closely.”

The Guardian reported on Saturday that demonstrators have continued to take to the streets of Iran, defying an escalating crackdown by authorities against the growing protest movement.

At least 62 people are reported to have been killed and 2,300 detained during weeks of protests sparked initially by anger over the country’s economy.

An internet shutdown imposed by the authorities on Thursday has largely cut off the protesters from the rest of the world, but some videos showed thousands of people demonstrating in Tehran overnight into Saturday morning. They chanted: “Death to Khamenei,” in reference to the supreme leader, Ayatollah Ali Khamenei, and: “Long live the shah.”

More than 570 protests have taken place across all of Iran’s 31 provinces, the US-based Human Rights Activists News Agency reported early on Sunday.

The speaker of Iran’s parliament on Sunday warned that the US military and Israel would be “legitimate targets” if America struck the Islamic Republic.

The comments, by Mohammad Bagher Qalibaf, represent the first to add Israel into the mix of possible targets for an Iranian strike.

Qalibaf, a hardliner, made the threat as lawmakers rushed the dais in the Iranian parliament, shouting: “Death to America!”