The Shadow Home Secretary said the economic debate “heightened” the discussion about immigration and compared the atmosphere to Germany between 1919-1933.
Speaking to an audience in London, she said: “Economic collapse has always led to scapegoating the other.
“The debate around immigration has been incredibly heightened by the economic consequence of the 2008 crash.
“Historically such as in the period of the Weimar Republic in Germany between the wars, economic collapse has always led to scapegoating the other.”
But her remarks have caused fury among MPs.
Conservative MP for Kettering Philip Hollobone said: “Diane Abbott has always been wrong about immigration and her latest remarks demonstrate how completely out of touch she is with the majority of public opinion out there in the real world.
“I’m afraid her London centric anti-Brexit views appear to be more warped than ever.”
Ms Abbott also pledged that Labour would allow parents of child refugees to join them in the UK.
But people warned that such a decision would lead to more deaths in the Mediterranean with families sending unaccompanied children to make the perilous journey alone.
The Shadow Home Secretary added: “This commitment underlines our commitment to human rights. This is the application of Labour values and it is the right thing to do.”
A spokesman for the Conservative Party said this would put lives at risk, adding: “Labour’s policy would risk breaking up families, creating a dangerous incentive for children to make the perilous journey across the Mediterranean and on to the UK on their own.
“Our immigration policy will always support those in genuine need and those who need the most.”
But Ms Abbott said most migrants were driven by the need to escape desperate conditions they were living in rather than “pull” factors.
She said: “The ‘push’ factors on migrants far outweigh any other issue.”
Ms Abbott claimed immigration is a euphemism for race and Labour should not be afraid to fundamentally change the conversation about the benefits of migration.
Speaking at King’s College London’s Policy Institute, she recalls the time she heard Enoch Powell’s “rivers of blood” speech 50 years ago.
She said: “I remember Enoch Powell’s speech, I think I was in primary school, and I wasn’t following it in huge detail, but I do remember how I felt.
“People were talking about it even in school and I felt frightened. I didn’t quite know why, I didn’t know exactly what had been said, but I felt frightened.
“And of course, one of the issues around immigration in some political quarters is that immigration is a euphemism for race, and you can’t have a serious debate around immigration unless you are prepared to face up to that.”