Andy Burnham told Sky News: "As the man who does uphold the independence of broadcasters in this country, I think it's right that broadcasters come to their own judgement.
"The fact that Sky are obviously still considering those issues in the balance, it does demonstrate that broadcasters that have an international presence, it's a difficult judgement call for them."
He was speaking after a string of politicians including International Secretary Douglas Alexander, Communities Secretary Hazel Blears and opposition spokesmen urged the BBC to reconsider its position.
Their comments drew criticism from BBC Trust chairman Michael Lyons who said some were "coming close to constituting undue interference in the editorial independence of the BBC".
Dr Sentamu remains unconvinced by the BBC's argument about impartiality
Earlier on Sunday, Liberal Democrat leader Nick Clegg accused the BBC of getting its priorities "upside down".
He told BBC's Andrew Marr show it was an "insult" to the viewing public to suggest they could not distinguish between humanitarian needs and political sensitivities.
So far, more than 50 MPs have backed a Parliamentary motion, to be tabled on Monday, urging the BBC to screen the appeal.
Meanwhile, the BBC has received about 1,000 complaints by telephone and a further 10,000 by e-mail.
The Church of England has also waded into the row, with the Archbishop of York appealing for the BBC to consider humanity, not impartiality, and show the film.
In a direct appeal to the BBC, Dr John Sentamu said: "Come on Auntie Beeb. Wake up and get on with it."
He went on to reject the argument that the BBC could be accused of bias if it were to screen the appeal.
"Why would it be taking sides when the appeal is not made by the BBC? It's not made by Hamas, it's not made by Israel, it's simply made by our disaster committee."
At a church service in Cambridge, the Archbishop of Canterbury, Dr Rowan Williams, said he endorsed Dr Setamu's views.
The Charity Commission, which regulates charities in England and Wales, echoed calls for the BBC to reconsider, saying the work of the agencies would be hampered without "maximum public support".
Andrew Hind, the commission's chief executive, said: "Oxfam, Save the Children, Islamic Relief are 100% confident they can convert aid and donations from the public into meaningful help to all those people in desperate need."
Dozens of demonstrators gathered in the reception area of the BBC Scotland headquarters in Glasgow on Sunday evening, protesting at the BBC's decision not to air the appeal.
On Saturday, thousands of protesters gathered outside the BBC headquarters in central London, where a petition was handed in calling for the film to be shown.
Later that same day, BBC director general Mark Thompson posted a blog on the BBC website explaining the decision.
He wrote: "Inevitably an appeal would use pictures which are the same or similar to those we would be using in our news programmes but would do so with the objective of encouraging public donations.
"The danger for the BBC is that this could be interpreted as taking a political stance on an ongoing story."
His comments generated hundreds of responses from readers of his blog, as thousands more entered a separate BBC website debate.
Greg Dyke, Mr Thompson's predecessor as BBC director general, said the issue had put the BBC in a "no-win situation".
"I can understand why the BBC has taken this decision, because on a subject as sensitive as the Middle East it is absolutely essential that the audience cannot see any evidence at all of bias," he told the Observer.
ITV, Channel 4 and Five will run the appeal for the first time on Monday.
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