The BBC has told a small number of senior staff to step back from their day-to-day duties on music and live events, following the broadcast of Bob Vylan’s controversial Glastonbury set.

The punk duo led a chant of “death, death to the IDF [Israel Defence Forces]” during their performance, which was available to watch via a live stream on iPlayer.

In a statement, the BBC said it was taking action to “ensure proper accountability for those found to be responsible” for the broadcast.

The BBC also said Bob Vylan were one of seven Glastonbury acts it had deemed “high risk” in advance of the festival.

The broadcaster said it would make “immediate changes to livestreaming music events”, so that “any music performances deemed high risk by the BBC will now not be broadcast live or streamed live” in the future.

The corporation’s chair, Samir Shah, said the decision not to pull the live feed was “unquestionably an error of judgement”.

Earlier on Thursday, Culture Secretary Lisa Nandy told the House of Commons she was unsatisfied with the BBC’s response after she had asked questions about due diligence, senior oversight, and the delay in pulling the live feed.

“Given the seriousness of what happened, and particularly we heard in the House the absolute shocking stories of the impact this has had on the Jewish community in this country – given the seriousness of this, I would expect there to be accountability at the highest levels [of the BBC],” she said.

The BBC has also been criticised by the UK’s chief rabbi Sir Ephraim Mirvis, while media regulator Ofcom said the corporation had “questions to answer”.

In a message to staff on Thursday, director general Tim Davie said: “I deeply regret that such offensive and deplorable behaviour appeared on the BBC and want to say sorry – to our audience and to all of you, but in particular to Jewish colleagues and the Jewish community.”

The BBC said Bob Vylan had been deemed high risk following a risk assessment process applied to all acts appearing at Glastonbury.

The duo, along with six other acts, were included in this category, but the BBC said they “were all deemed suitable for live streaming with appropriate mitigations”.

The statement continued: “Prior to Glastonbury, a decision was taken that compliance risks could be mitigated in real time on the live stream – through the use of language or content warnings – without the need for a delay. This was clearly not the case.”

The BBC noted that the live stream was monitored “in line with the agreed compliance protocols and a number of issues were escalated”.

Warnings appeared on the stream on two occasions, but, the BBC added: “The editorial team took the decision not to cut the feed. This was an error.”

Davie, who was attending Glastonbury himself on the day, was “subsequently made aware of what had happened and instructed the team that none of the performance should feature in further coverage”.

The BBC said the team on duty prioritised stopping the performance from becoming available on demand, meaning that the set would not appear separately on iPlayer or BBC Sounds.

However, the live feed remained available for more than four hours, which meant viewers were able to rewind and view the content.

“Given the failings that have been acknowledged, we are taking actions to ensure proper accountability for those found to be responsible for those failings in the live broadcast,” the BBC said. “We will not comment further on those processes at this time.”

In a statement, Shah apologised “to all our viewers and listeners and particularly the Jewish community for allowing the ‘artist’ Bob Vylan to express unconscionable anti-semitic views live on the BBC”.

“This was unquestionably an error of judgement,” he added. “I was very pleased to note that as soon as this came to the notice of Tim Davie – who was on the Glastonbury site at the time visiting BBC staff – he took immediate action and instructed the team to withdraw the performance from on demand coverage.”

Since Glastonbury, Bob Vylan have had several bookings cancelled, including festival appearances in Manchester and France and a slot in Germany.

In response to the cancellations, the band reiterated their position, telling followers: “Silence is not an option. We will be fine, the people of Palestine are hurting.”

Avon and Somerset Police have launched a criminal investigation into their Glastonbury comments.

On Wednesday, London’s Metropolitan Police said the band are also under investigation for comments they allegedly made during a concert at Alexandra Palace in May.

During their Glastonbury set, Bob Vylan’s singer Pascal Robinson-Foster, who performs under the stage name Bobby Vylan, also spoke about a record label boss he used to work for.

That boss would “speak very strongly about his support for Israel”, and had put his name to a letter urging Glastonbury to cancel Irish-language rap trio Kneecap’s performance, the musician said.

“Who do I see on that list of names but that bald-headed [expletive] I used to work for. We’ve done it all, all right? From working in bars to working for [expletive] Zionists.”

After the media coverage of their comments, Bob Vylan said in a statement on Tuesday: “We are not for the death of Jews, Arabs or any other race or group of people. We are for the dismantling of a violent military machine”.

They added that “we, like those in the spotlight before us, are not the story. We are a distraction from the story, and whatever sanctions we receive will be a distraction”.