The broadcaster also confirmed that the programme will not be shown again.
A BBC spokesperson said: "While the BBC sincerely regrets the manner in which the video clip was edited, we strongly disagree there is a basis for a defamation claim."
A letter dated Nov. 9 sent to the BBC by lawyers acting for Trump demands that the BBC should issue "a full and fair retraction of the documentary", apologize, and "appropriately compensate" Trump for "the harm caused."
The letter said the BBC should comply with the demands by Friday evening, or face "legal action" for no less than 1 billion U.S. dollars in damages.
The program was criticized for splicing together clips of Trump's speech on Jan. 6, 2021 in a way that allegedly gave the misleading impression that he urged his supporters to march to the U.S. Capitol and "fight like hell."
Xinhua