“I think we have to have the person who is most likely to beat Jeremy Corbyn and I think that’s me”, said Eagle while sitting alongside Smith on the same programme.
Ms Onwurah, MP for Newcastle upon Tyne Central, made the comments as the contest to see if Mr Corbyn stays on as leader continued.
The leadership contest was triggered on Monday when lawmaker Angela Eagle challenged Mr Corbyn. The Lancashire-born MP has leapfrogged Eagle and is now the second-favourite to win the upcoming election, with his chances improving with each day that passes.
And only 23% think the current leader has what it takes to be prime minister but just 21% think Ms Eagle would make a good PM.
Many Labour MPs believe she did the courageous ground work that cleared the way for Owen Smith.
The former shadow work and pensions secretary, however, reveals he had suggested to Corbyn that he could become president or chair of Labour, in return for standing down. “But unfortunately that leadership did not emerge”.
Turning Mr Corbyn’s “kinder politics” catchphrase against him, Ms Eagle said that Labour needed “a kinder politics in reality” and must not end up “in the gutter”.
Last night, Labour’s largest individual donor, John Mills, who has given more than £1.6 million to the party, said: ‘I am aware of these sorts of discussions, but I am very reluctant to get involved in the plots and schemes.
They are what the grass roots of the Labour Party is about and why I joined almost 50 years ago, and what I have worked for ever since.
He will also warn the party risks “falling apart” if it does not act “like a proper team”, and is expected to attack Mr Corbyn for being anti-austerity without bringing forward an alternative.
The former shadow business secretary, who quit the shadow cabinet to launch her challenge to Mr Corbyn, asked party members at a social event in Wolverhampton: “What attracted you to the Labour Party in the first place?”
Despite polls showing a huge deficit in leadership and competence ratings to the new Prime Minister, Mr Corbyn added that “of course” he could lead Labour to a general election victory against Theresa May.
“We urge all Labour MPs to unite the party behind his leadership and focus our energies on challenging the Conservatives and presenting policy that will help the many communities who need a Labour Government”.
“It is a moment in which I think we all understood if any of us were still under any misapprehension that Iraq was a awful mistake”. Owen Smith has benefited – from where the membership is – by having a less confrontational role, but I hope fortune favours the fearless.