BBC Trust chairman Michael Lyons has voiced concerns over political interference in the BBC's editorial independence, after a number of politicians publicly criticised the move.
The Disasters Emergency Committee (DEC) appeal will be screened for the first time on Monday.
In a blog message on the BBC website explaining the decision, Mark Thompson said: "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."
He stressed the corporation would "continue to cover the human side of the conflict in Gaza extensively across our news services where we can place all of the issues in context in an objective and balanced way".
He also cited another reason for the decision as "concern about whether aid raised by the appeal could actually be delivered on the ground".
We can't ignore suffering in the interests of what the BBC call impartiality
Andrew Hind, chief executive of the Charity Commission, which regulates UK-registered charities, said all the leading agencies in the DEC have said they can deliver.
"That is not an issue for them," he 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."
He urged the BBC to reconsider and said the work of the agencies would be hampered if they did not receive "maximum public support".
Earlier on Saturday, police said at least 2,000 protesters gathered outside the BBC's Broadcasting House in central London before handing in a petition to the corporation.
There were seven arrests at the rally.
Earlier, ITV and Sky had been in agreement with the BBC that they would not air the appeal. But ITV later reversed its decision.
Sky says it is still considering the Disasters Emergency Committee's request.
The DEC - an umbrella organisation for several major aid charities - wants to raise funds for people in need of food, shelter and medicines as a result of Israel's military action in the Gaza Strip.
Previous DEC appeals shown on multiple TV and radio channels have raised millions of pounds for victims of wars and natural disasters.
International Development Secretary Douglas Alexander said the British public could "distinguish between support for humanitarian aid and perceived partiality in a conflict".
"I really struggle to see in the face of the immense human suffering of people in Gaza... that this is in any way a credible argument," he added.
BBC's chief operating officer Caroline Thomson defends the veto
Shadow international development secretary Andrew Mitchell said it was "clearly a decision for the BBC and other broadcasters " whether they showed the appeal.
Liberal Democrat leader Nick Clegg said it was an "insult" to the viewing public to suggest they could not distinguish between humanitarian needs and political sensitivities.
Speaking on the BBC's Andrew Marr show, he said: "To suggest the BBC should somehow not allow people to show their compassion... because of the wider controversies in the Middle East, is a case of the BBC totally getting its priorities upside down."
In a letter to the BBC director general on Saturday, BBC Trust chairman Michael Lyons expressed concern that the "level and tone" of some of the political comment was "coming close to constituting undue interference in the editorial independence of the BBC".
He assured Mr Thompson the Trust would "do everything in our power to ensure that you are given the space to make the editorial decisions you feel, after due consideration, are right in the circumstances".
BBC political correspondent Gary O'Donoghue said the corporation was facing "quite a lot of pressure", but its position had been shored up "a little bit" by the Trust's move.
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