The NEC on Tuesday agreed that Mr Corbyn will automatically appear on the leadership ballot but introduced restrictions on who will be able to vote in the contest, which his rivals hope will benefit them.
Owen Smith, who is running for leadership in the Labour party, has promised to call a new referendum on European Union membership if elected, in an interview to the Guardian newspaper.
He went on: "I think there are many people out there who voted in good faith for Brexit and who felt they were doing the right thing for their families and their communities and I respect them for taking that decision", he said. The need to end the privatisation of our National Health Service.
Labour-commissioned analysis said Mr Corbyn needed nominations from MPs to stand again.
Reaching the target of 51 would have been by no means certain as many of his MPs recently voted against him in a no-confidence motion.
Labour's former work and pensions spokesman Owen Smith has said he would consider making a rival leadership challenge.
Shadow Business Minister Eagle welcomes the contest she says she will win.
Last year, shortly after Corbyn won an overwhelming mandate from Labour party members, Foster stood at the back of a Labour Party conference fringe meeting in Brighton shouting: "Say the word "Israel, ' say the word 'Israel, '" after Corbyn addressed LFI supporters".
Wallasey MP Angela Eagle is expected to join Mr Corbyn in the leadership race, while Pontypridd MP Owen Smith has also been suggested as a possible candidate.
Labour rebels were left infuriated by the decision, claiming the trade unions had "done us over" by propping up Mr Corbyn and saying he does not have the "moral authority" to lead. I welcome the contest ahead.
The power struggle within the Labour peaked when his leadership was challenged by party lawmaker Eagle on Saturday.
Sharpe added that whether Corbyn would still be leader by the time another General Election rolls around was a different matter, with odds of 8/13 that he would, 6/5 that he'd be out before then.