"The public wants us to be very strict about our impartiality and it is my job to protect that impartiality," he said, denying that his "arm had been twisted" by pro-Israeli lobbyists.
Thompson said: "Our viewers will find out a great deal about this appeal on BBC news programmes, I'm sure there will be a link to the appeal on our website.
"Potentially many millions of people will find out about this appeal through the BBC. What we're not going to do is run a free standing appeal on our airwaves."
The British-based Sky News channel joined the BBC on Monday in refusing to broadcast the emergency appeal, intended for victims of Israel's 22-day military offensive on the Palestinian territory.
John Rylye, Sky News director, said: "The conflict in Gaza forms part of one of the most challenging and contentious stories for any news organisation to cover.
"Our commitment as journalists is to cover all sides of that story with uncompromising objectivity."
Other British broadcasters, including Channel 4, ITV and Five, have said that they will show the appeal.
Many aid groups have been strongly critical of the BBC's decision not to televise the advertisement.
"By declining their request, the BBC has already taken sides and forsaken impartiality," said John Sentamu, the Archbishop of York and the second most senior Anglican clergyman.
Steven James, an organiser for the UK-based medical aid for Palestinians organisation, told Al Jazeera: "This is about helping women, children and civilians caught up in the situation, in a time when they really need aid.
"Quite frankly, we are astonished at the BBC."