"I think we need to clear the air. I think whoever wants to stand for leader of the Labour Party should do so and we should have a good debate about the direction of the party and the government."
She insisted that she did not have a particular candidate in mind.
But she told BBC Radio 4's PM programme that "a huge number of Labour MPs want a leadership election".
She refused to say whether she would back Gordon Brown or another candidate in a contest.
Asked if Mr Brown had done a good job since taking over, she said: "I think Gordon Brown is a really good man who has the best of intentions. I just think that being prime minster is a shockingly hard job."
The Labour Party is quite clearly degenerating into a state of civil war
Chris Grayling Shadow cabinet member
Asked whether she felt he was "shockingly bad" at it, she said not.
Ms McDonagh is so far the only member of the government to call publicly for a leadership contest.
She added: "If I could have found an easier way, or a quieter way, to do this then I would have done it.
"But everyone's saying, 'You first.' I didn't want to be in a position where I'd look back in five years' time and think I could have done the right thing but didn't do it."
She is among a small group of Labour MPs to have sought details about the nomination process for a contest.
She told PM she had written to Labour's general secretary in confidence to ask for nomination papers but had been forced to go public with her concerns after being contacted by a journalist.
Labour confirmed the party had received letters from a "small number" of MPs asking why no nomination papers for leader were issued ahead of the party conference.
It would take 70 MPs to trigger a potential leadership contest.
Labour MP Emily Thornberry mounted a defence of Mr Brown's premiership on PM, saying the public would not "respect" Ms McDonagh for her call.
And the reason no alternative candidate had come forward to challenge Mr Brown was that he was "best qualified" to steer the country through difficult economic times, she said.
But Chris Grayling, for the Conservatives, said: "The Labour Party is quite clearly degenerating into a state of civil war.
"For a prime minister to have one of his own whips calling for a leadership contest is unprecedented.
"At a time when Britain faces massive economic challenges it is profoundly damaging to have a government in such disarray. We need an early election to get the change Britain so desperately needs."
'Hammer blow' warning
In a separate development, 12 backbench Labour MPs, including six former ministers, have urged the leadership to develop "a convincing new narrative" which has to be more than "a series of policy initiatives" in order to restore Labour's fortunes.
In a joint article for New Labour magazine Progress, they say Labour has "no explanation yet" as to how it will "steer the economy through the troubled waters ahead".
And they claim that "one-off taxes and pay-outs, no matter how justified in their own terms, do not amount to a strategy", adding there is a "yawning chasm" which the Labour party needs to fill or the government will suffer a "hammer blow".
The piece is signed by Janet Anderson, Karen Buck, Patricia Hewitt, George Howarth, Eric Joyce, Sally Keeble, Stephen Ladyman, Martin Linton, Shona McIsaac, Margaret Moran, Tom Levitt, and Paddy Tipping.
Progress insists the article it is not linked to Ms McDonagh's call for a leadership contest but it will add to pressure on Gordon Brown ahead of Labour's conference later this month.
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