The Normanton, Pontefract and Castleford MP warned that the Donald Trump approach to politics was “normalising hatred” and the problem was not confined to the right wing.
She highlighted the “unacceptable” and “utterly shameful” abuse directed at Labour MP Luciana Berger, who has been targeted by supporters of Mr Corbyn over her past criticism of the leader.
And she also defended BBC political editor Laura Kuenssberg, who has been subjected to vitriol from all sides.
Ms Cooper, who will again chair the influential Commons Home Affairs Select Committee after being elected unopposed, said the “kinder, gentler” politics espoused by Labour leader Mr Corbyn must be part of the party’s path to power.
Her four-point plan also involves staying a “broad-based party” - a clear warning to the Labour left which is stepping up moves towards forcing MPs to face a mandatory reselection process, viewed by some on the right as an attempt to oust them in favour of Corbyn loyalists.
Labour must also chart a course for a “progressive Brexit”, and overcome the “new and growing divide” between cosmopolitan and thriving cities and the smaller towns which are struggling.
Ms Cooper, speaking at the Fabian Society conference in London just hours after Theresa May met Donald Trump in the margins of the G20 summit, lashed out at the US president and condemned the Prime Minister’s failure to speak out against him.
Referring to Mr Trump’s use of Twitter, she said: “These aren’t just harmless rants from a sad man in his bedroom.
“This is the bully pulpit of the most powerful man on the planet, broadcast direct to millions of people, echoed and amplified by the Breitbarts, the cheerleaders, the echo chambers.”
Ms Cooper, who set up the Reclaim The Internet campaign to challenge online abuse, said she was “sick to death of the vitriol poured out from all sides towards Laura Kuenssberg”.
“It is her job to ask difficult questions. It is her job to be sceptical about everything we say. Nothing justifies the personal vitriol, or the misogyny.”
Condemning the abuse aimed at Liverpool Wavertree MP Ms Berger, Ms Cooper said: “Frankly Labour Party members should be united in supporting Luciana, not targeting her or trying to intimidate her. Unacceptable always in the Labour party. Utterly shameful against someone who has stood up to fascists, someone who is on maternity leave.
“Nor is there any excuse for vitriolic abuse against our opponents. During this general election campaign some Tory women MPs and candidates were targeted with unacceptable personal abuse from the left.
“And we’ve seen Labour supporters at rallies holding placards with the severed head of Theresa May.
“Maybe it was meant as a joke. It isn’t funny.”
She said she felt “huge anger” at what Mrs May was doing “but I never ever want to see Labour people mocking up pictures of her head on a stake”.
“I never ever want our party to dehumanise our opponents. That’s what the far right do.”
She pointed out that Labour had “already lost someone to hatred” when Jo Cox was murdered by a far-right extremist last year.
“I believe there is a real appetite now for the politics of kindness and humanity. Jeremy understood that two years ago when he talked about the kinder, gentler politics,” she said.
Normanton, Pontefract and Castleford MP Ms Cooper vowed to use the hung parliament to “seize any chance” to push for the restoration of the Dubs Amendment requiring the Government to take in vulnerable child refugees.
Labour would also use the situation in the Commons “to hound government ministers for every dangerous move they make” and “halt every mad policy they try to impose”.
She said: “The Tories are still in government even if they aren’t properly in power. Their weakness is making them desperate. For our country, their desperation makes them dangerous.”