The corporation has resisted pressure to follow rival channels ITV, Channel 4 and Five who are to show the DEC film.
It says it would put its reputation for impartiality at risk, but other ministers and the Archbishop of York have urged the BBC to air the appeal.
BBC Trust chairman Michael Lyons has voiced fears of political interference.
On Thursday it emerged that the publicly-funded BBC had decided not to broadcast British charities' appeal to raise funds to help thousands in Gaza without food or medicine.
ITV and Sky had agreed with the BBC, but ITV later reversed its decision. Sky says it is still considering the Disasters Emergency Committee's request.