Police have formally opened a criminal investigation into comments made by Bob Vylan and Kneecap at Glastonbury after reviewing video and audio footage of the performances.

Avon and Somerset police said the performances had been recorded as a “public order incident at this time” and the investigation would “consider all appropriate legislation, including relating to hate crimes”. A spokesperson added: “There is absolutely no place in society for hate.”

Pascal Robinson-Foster, of the punk-rap duo Bob Vylan, led chants of “Death, death to the IDF”, referring to the Israel Defense Forces, and spoke of working for a “fucking Zionist” during their show on the West Holts stage on Saturday.

The Irish rap trio Kneecap followed the group with an incendiary performance that included leading the crowd in chants of “fuck Keir Starmer”.

Earlier on Monday the BBC said it regretted not cutting the live stream of Bob Vylan’s performance, saying it contained “utterly unacceptable” antisemitic sentiments, while the US announced it was revoking visas for the band.

The BBC initially acknowledged that some of the comments were “deeply offensive”. It said a warning was issued on screen about the “very strong and discriminatory language” at the time.

However, the BBC went further on Monday, saying it should not have allowed the comments to be broadcast and would look to update its guidance around live events.

“Millions of people tuned in to enjoy Glastonbury this weekend across the BBC’s output but one performance within our livestreams included comments that were deeply offensive,” it said. “The BBC respects freedom of expression but stands firmly against incitement to violence. The antisemitic sentiments expressed by Bob Vylan were utterly unacceptable and have no place on our airwaves.

“The team were dealing with a live situation but with hindsight we should have pulled the stream during the performance. We regret this did not happen.”

The comments came after pressure from Starmer, Ofcom and the culture secretary, Lisa Nandy, who questioned Davie over the weekend over what due diligence had been done in advance of the broadcast. The prime minister’s spokesperson said there was “no excuse for this kind of appalling hate speech, and the BBC needs to explain how these scenes came to be broadcast”.

Meanwhile, the band, who had been due to tour America later this year, have had their US visas revoked. “Foreigners who glorify violence and hatred are not welcome visitors to our country,” said Christopher Landau, the deputy secretary of state.

Warren Stephens, the US ambassador to the UK, said the chants were a “disgrace”, adding: “There should be no place for this hateful incitement or tolerance of antisemitism in the UK.”

The band appear to have been dropped by the talent agency UTA and their page was no longer active on the agency’s website.

In an urgent statement in parliament, Nandy said members of the Jewish community at the festival had said they created “their own safe space” because of the imagery on display.

She said she was not satisfied with the explanation she had been given by the BBC so far over the broadcast, and she called on the corporation to “quickly and swiftly” answer a list of specific questions from her officials.

“Much of this was foreseeable,” she said, saying basic online research would have shown potential issues with the Bob Vylan broadcast.

Writing on Instagram on Sunday, Robinson-Foster said his phone had been “buzzing non-stop, inundated with messages of both support and hatred”.

He said: “Teaching our children to speak up for the change they want and need is the only way that we make this world a better place. As we grow older and our fire starts to possibly dim under the suffocation of adult life and all its responsibilities, it is incredibly important that we encourage and inspire future generations to pick up the torch that was passed to us.”

Kneecap, meanwhile, shared a post on social media on Monday night highlighting the situation in Gaza.

Bob Vylan’s performance was not broadcast on linear television but could be watched on Saturday via a livestream on iPlayer. The BBC opted not to broadcast the livestream of the Irish rap artists Kneecap, who appeared later on the same West Holts stage as Bob Vylan.

Ofcom said the BBC “clearly has questions to answer” after livestreaming the Bob Vylan footage. “We have been speaking to the BBC over the weekend and we are obtaining further information as a matter of urgency, including what procedures were in place to ensure compliance with its own editorial guidelines,” it said.

Glastonbury festival had earlier condemned the chants started by Bob Vylan, saying organisers were “appalled by the statements” made on stage.

Starmer condemned the band’s performance over the weekend, describing it as “appalling hate speech”. Chris Philp, the shadow home secretary, went further, asking police to “urgently investigate and prosecute the BBC” for broadcasting it.

UK Screen Industry, a group of concerned TV and film professionals, said: “We reject the BBC’s statement that Bob Vylan’s words were ‘antisemitic’ and an ‘incitement to violence’. Saying ‘Death to the IDF’ is not a literal threat; it is a call for the dismantling of a brutal military apparatus that is committing war crimes and killing civilians.”

Avon and Somerset police said: “We have received a large amount of contact in relation to these events from people across the world and recognise the strength of public feeling. We politely ask the public refrain from continuing to report this matter to us because an investigation is already taking place.”