Eagle, who will today formally launch her bid to take over the left-of-centre party, said Corbyn was “not a leader” and she wanted to “heal” Labour’s divisions.
Both Labour and Prime Minister David Cameron’s ruling Conservative party have been plunged into turmoil by Britain’s shock referendum vote to leave the EU last month.
Corbyn faced criticism from within the party for his lukewarm campaigning in favour of Britain staying in the EU. In a vote of confidence on June 28, Corbyn received the backing of only 17% of his colleagues in parliament.
“I don’t think he’s been able to communicate with the electorate,” Eagle, the party’s former business spokeswoman, told ITV television.
“He cannot continue in the job because he’s lost the confidence of the Parliamentary Labour Party and he’s hiding behind a closed door, denying that this is a fact. That’s not leadership.”
Corbyn said he was “disappointed” by Eagle’s challenge and urged her to “think for a moment” about her actions.
The leadership contest will hang on whether the party’s National Executive Committee (NEC) decides Corbyn should have an automatic place on the ballot and does not require a minimum number of MPs supporting him — something he would struggle to achieve.
There is debate within the party as to how its leadership challenge rules should be interpreted.
“I’m expecting to be on the ballot paper,” Corbyn told BBC television.
He said if the NEC decided he needed nominations, “I will challenge that if that is the view they take”, adding: “I’ve taken much soundings from lawyers”.
Conservative party members will also vote later this year to elect a successor to Cameron, who announced he would quit after losing the EU vote.
The choice between Interior Minister Theresa May and junior Energy Minister Andrea Leadsom means Britain will have its first female prime minister since Margaret Thatcher.
Corbyn also indicated he would back a motion to find Labour former prime minister Tony Blair in contempt of parliament over his role in the war in Iraq.
“Parliament must hold to account, including Tony Blair, those who took us into this particular war.” Asked if he would back the motion, he said: “I haven’t seen it yet, but I think I probably would.”
