The shadow cabinet minister, a long-time ally of Mr Corbyn, told party activists that critics of the Labour leader were exploiting his “vulnerability” over the row on handling cases of anti-Jewish hate.
Mr Corbyn is facing renewed pressure over the party's long-running antisemitism row, after several former staffers broke cover to tell a BBC documentary that senior figures had intervened in the handling of complaints.
Meanwhile Labour peers are understood to be gearing up for a confidence vote in Mr Corbyn next week after Baroness Hayter, Labour’s deputy leader in the Lords, was sacked for comparing the mood in the leader’s office to the “last days of Hitler”.
She was among a group of peers who criticised the leadership for its response to the Panorama documentary. Labour has denied the allegations and complained to the BBC about potential editorial bias.
At a meeting in her Hackney constituency, Ms Abbott rejected accusations that Labour was now “systematically racist” and said the “same elements have challenged him all along”, according to a record obtained by HuffPost.
“Jeremy has had to go through two leadership challenges. Both times he had the absolute might of the establishment of the British state against him,” she said.
“And I am afraid it may be, that if what we are hearing and seeing in the past few weeks, we may have to go through a third leadership challenge.”
Ms Abbott said the “incredible onslaught” of antisemitism complaints were occurring as Mr Corbyn’s critics were “so terrified” of him becoming prime minister.
She told the meeting: “Jeremy is the most strongly anti-racist person I know and he certainly is not an antisemite.
“Of course, there is antisemitism in the Labour party. But the Labour party is not a systemically racist party as some of our own colleagues would have you believe.”
Labour MP Wes Streeting told The Independent that the comments reflect a ”wider paranoia” that concerns about antisemitism are motivated by wanting to attack Mr Corbyn.
“They need to wake up and realise that the reason why people like me are so angry and upset is because we are morally appalled by what is going and want it fixed,” he said.
“That’s what leadership is all about and instead of feeling sorry for themselves and bunkering down they just need to fix the bloody problem.”
Meanwhile, Labour peers will meet on Monday to discuss whether to hold a vote of no confidence in Mr Corbyn after the sacking of Baroness Hayter. Such a vote would be non-binding on Mr Corbyn.
She told a meeting of the centre-left Labour First group: “Those of you who haven’t [read the book] will have watched the film ‘Bunker’, about the last days of Hitler, of how you stop receiving into the inner group any information which suggests that things are not going the way you want.”
A Labour Party spokesman said: “Dianne Hayter has been sacked from her frontbench position with immediate effect for her deeply offensive remarks about Jeremy Corbyn and his office.
“To compare the Labour leader and Labour Party staff working to elect a Labour government to the Nazi regime is truly contemptible, and grossly insensitive to Jewish staff in particular.”