The ex-shadow business secretary called on Mr McDonnell to sign a clean campaign pledge after his comments.
Mr McDonnell won loud cheers at a pro-Corbyn fundraising event after he denounced those seeking to force a change in leadership.
“They have been plotting and conniving. The only good thing about it, as plotters they’re f****** useless,” he said to loud cheers.
The shadow chancellor later insisted his remarks were a “joke” and he was not referring to Ms Eagle.
But Ms Eagle said the comments “speak for themselves” and had “disfigured” the leadership race as she signed a “keep it comradely” campaign pledge at Westminster.
“We don’t want to have a debate that is disfigured by bullying, intimidation, threats, or the kind of language that John McDonnell used last night,” Ms Eagle said. “This is my clean campaign pledge and I hope all the other candidates in the leadership election and their supporters will sign up to this pledge.
The shadow chancellor insisted his remarks were not meant to be taken seriously, saying: “It was a stand-up comedy event. It was a joke. It was taken in a light-hearted way.” He insisted Mr Corbyn had not made a big fuss over “death threat after death threat” that he had received since becoming leader.
Mr McDonnell said he was referring to a small, hard-core group in the party who had never accepted Mr Corbyn’s leadership, when he made the remarks.
Anti-Corbyn MPs have accused Mr McDonnell of moving to block a “peace deal” for an orderly transition of power by talking Mr Corbyn out of resigning in the wake of the vast majority of the parliamentary party voting no confidence in his leadership.
Mr Corbyn has insisted he is “going nowhere” and intends to honour the mandate given to him by 59.5 per cent of party members in last September’s leadership election.
Meanwhile, veteran former minister Dame Margaret Hodge accused Mr Corbyn and his supporters of engaging in “dirty politics” as the party faced a bitter leadership battle set to eat up its energy over the next two months.