The Labour party has called for the resignation of South Yorkshire's police and crime commissioner, Shaun Wright, in the wake of the child sex abuse scandal in Rotherham.

Wright was a Labour cabinet member for children and young people's services at Rotherham council from 2005 to 2010 when he received three reports about widespread abuse but failed to act, according to Prof Alexis Jay's damning report on the sexual exploitation of 1,400 children over 16 years in the South Yorkshire town.

Speaking publicly for the first time since the report was published, Wright insisted on Wednesday that he had acted properly, and rejected calls for him to go.

Wright told the BBC: "The scale of the problem has come as a surprise to me." He said he was not aware of the "industrial scale" of the abuse.

As he defended his position, a Labour party spokesman told reporters asking for Ed Miliband's view on the matter that Wright should quit. "The report into child abuse in Rotherham was devastating in its findings. Vulnerable children were repeatedly abused and then let down. In the light of this report, it is appropriate that South Yorkshire police and crime commissioner Shaun Wright should step down," he said. The call has been echoed by David Blunkett, the former Labour home secretary and Sheffield MP.

Ed Balls, the shadow chancellor, told BBC radio's The World at One that Wright should stand down because "of the failures of leadership". He said: "It's important that people in positions of responsibility take responsibility."

Speaking later to Sky News, Wright insisted he had already taken responsibility for the failures at the council by standing down as cabinet member for children's services in 2010.

"The report clearly identifies systemic failure. I was part of that organisation at the time and I took that responsibility very seriously. I stood down in 2010 from that particular role, then I subsequently became the South Yorkshire police commissioner. I have taken those lessons and brought them to bear on South Yorkshire police here and now."

He added: "I'm very sorry for any abuse that took place. If I could have prevented it I would. This is a top priority for South Yorkshire police. I take my share of the responsibility. If I knew then what I know now then clearly more could have been done. I do have regrets that I wasn't more aware of the issue at the time. I regret my role in that systemic failure and have taken my responsibility for that.

"As a responsible parent, a responsible adult, I'm doing everything in my power to make this adequately tackled here in South Yorkshire."

Before he was elected police and crime commissioner in 2012, Wright was also a member of the South Yorkshire police authority. Jay's report exposed repeated failures in both the council and the police to tackle the abuse.

Rotherham's Labour council leader, Roger Stone, resigned within hours of the publication of Jay's report.

There have been repeated calls for Wright to do the same. Education minister Nick Gibb said those responsible for policy decisions which contributed to the scandal "should be held to account".

He told ITV News: "It is quite appalling that the more vulnerable the children, the more horrific their stories, the less they are believed by the statutory authorities. And those that took those policy decisions I think should be held to account."

Paul Lakin, the deputy leader of the council and Wright's successor as cabinet member for children's services, refused to say whether he thought the commissioner should go.

But he offered only partial backing as he spoke to BBC Radio's 4 Today programme. "The decision on whether the police and crime commissioner should go is clearly an issue for him and for him alone. There are clearly people who are either councillors within the council or working for other authorities who really need to take a look at their role throughout this time and then decide on their position.

"Commissioner Wright, since he has been in his current role, has taken an active view on sexual exploitation and has put in a lot of resources to tackle this. Some may say that's a little too little and too late, but I'm not going to give you a view on whether he should resign, that's clearly down to him.

"We need to go through the report in depth. Clearly governance arrangements came out as one of the issues."

Lakin, himself a councillor since 1999, said he had not been aware of the depth and scale of child abuse in Rotherham until the publication of Jay's report.

Colin Ross, the leader of Sheffield's Liberal Democrat party, said: "It's difficult to see how people can have confidence in him [Wright] to continue."

Ukip's Yorkshire and Humber MEP, Jane Collins, added: "I categorically call for the resignation of everyone directly and indirectly involved in this case. The Labour council stand accused of deliberately ignoring child sex abuse victims for 16 years. The apologies we have heard are totally insincere and go nowhere near repairing the damage done.

"These resignations should include South Yorkshire's police and crime commissioner, Shaun Wright. I also call for a criminal investigation by a force not directly linked with this scandal into all those implicated in this scandal. There is no place for these people in public life."

Twitter was awash with angry tweets at Rotherham's failure to tackle the abuse, singling out Wright for particularly criticism.

Fathers 4 Justice, the campaign group for the rights of fathers, tweeted that Wright had failed hundreds of children.

Andrew Morley, the former chairman of the London Criminal Justice board, said Wright's position was "untenable".

Jay's report did not criticise Wright directly but it noted that he passed on concerns to other bodies and called for further investigations after receiving reports about widespread child abuse in Rotherham.

Earlier Wright had issued an apology for the council's failures but refused to discuss his future.

In a statement, his spokeswoman said: "The commissioner has previously apologised for the failure of Rotherham council while he was in its cabinet from 2005 to 2010. He repeats that apology today and he fully accepts that there was more that everyone at Rotherham council should have done to tackle this terrible crime.

"Since becoming police and crime commissioner he has repeatedly publicly made tackling child sexual exploitation his number one priority."

Conservative councillor Chris Middleton also called for Wright to stand down, describing his position as untenable.

Former children's minister Tim Loughton called for heads to roll. Speaking to the BBC's Newsnight programme, he said: "It is too common a theme, that when these scandals take place, be it in Haringey or Rochdale or wherever, that very few people actually pay the consequences and are sacked.

"We do need to look at the records of some of the people who were in positions of responsibility when this sort of abuse was going on, in Rotherham and in other places. It is not good just to say, 'Oh well, I wasn't there when this was happening.' At least the leader of the council has done the decent thing and stood down."