The former shadow home secretary - who revealed on Sunday that she had received online death threats - said Mr Corbyn should respond directly to trolls claiming to be party members or supporters of his leadership and tell them that he disapproves of their activities.
It was not enough for the Labour leader and shadow chancellor John McDonnell simply to say they want the bullying to stop, without taking “positive and active” steps to stop the perpetrators, she said.
Pontefract, Castleford and Normanton MP Ms Cooper, who has set up a Reclaim the Internet campaign to tackle online abuse, said: “I have asked Jeremy and the Labour Party to use their social media accounts to challenge people who seem to be Labour Party members, to challenge them and say ‘Not in our name, this is not what we expect’.
“As well as going through all the procedures, let’s also be positive and active in the way in which we challenge abuse as well. In the end this is about our values and our sense of our common humanity and our sense of respect and decency in politics.”
Speaking to a gender equality meeting hosted by teaching union NASUWT on the fringe of Labour’s annual conference in Liverpool, Ms Cooper denied that she was using the issue of abuse to score points in the internal struggle between the party’s left-wingers and moderates.
“This abuse has got to stop, wherever it comes from,” she said.
“The key challenge actually - the reason this is a challenge to the leadership of the party and the reason I have said Jeremy and John need to act about this - is not a factional point.
“It is because they are the leadership of this party that they must take some responsibility and act. It is because they can do so.”
Ms Cooper also called on the party leadership to implement a code of practice which has been adopted by Labour’s ruling National Executive Committee (NEC).
“We in the Labour Party have always stood up against oppression, intimidation and bullying, be it by the powerful or be it by the mob. How can we do that if we actually have a minority of people in our own party who are abusing others? Frankly some of the cases that the NEC have had to investigate have been vile and shocking,” she said.
“We know it’s a minority but nevertheless it should be dealt with and we need to have proper leadership to deal with it as well.
“That is why I have been calling for a new code of practice for 12 months, finally the NEC ... has agreed it, that now needs to be implemented and we need a proper code of practice and enforcement and resources to do it.”