"At least your dismal ratings can now allow you to concentrate on your airline which, I am sure, needs every ounce of your energy. It is obviously a terrible business and I can't imagine, with fuel prices etc, that you can be doing any better in it than anyone else," he writes.
Like television, you should try to get out of the airline business too, as soon as possible! Actually, I wonder out loud how you can be anywhere close to a billionaire and be in that business."
Adding: "Perhaps the title of your show, The Rebel Billionaire, is misleading?"
He ends the scathing note by taking one more jab at Branson's show.
"In any event, do not use me to promote your rapidly sinking show - you are a big boy, try doing it yourself!"
Branson replied with his own letter five days later, in a noticeably more diplomatic tone.
"Thanks for your note. I think if you look carefully through the press cuttings, I have actually avoided 'nasty' comments. I have enjoyed the time we have spent together and would not denigrate you personally," he wrote.
Branson said that many interviewers asked him questions about Trump and he told them that he didn't agree with some of Trump's "10 Rules for Success", particularly the advice to "go all out to get your own back on anyone who crosses you".
He calls out Trump for his own offensive remarks that he had been making in the media.
"I have read what I believe can be misconstrued as 'nasty' comments from you about myself in the press over the last couple of weeks and - although tempted - have to date decided not to respond to them and to rise above them," Branson writes.
In response to Trump's gibe about whether Branson could even be considered a billionaire he confirmed that he has "created six billion-dollar empires in six completely different sectors and I think that qualifies Fox to title this show 'The Rebel Billionaire'".
It is no secret that the two business tycoons have not always seen eye-to-eye.
Just before the Presidential election last year, Branson published a blog post describing his "bizarre" first encounter with Trump.
According to Branson, Trump had spent the whole lunch meeting talking about how he was going to get revenge on a list of people who had refused to help him when he was near bankruptcy.
He expressed concerns that Trump's "vindictive streak" could be "so dangerous if he got into the White House", sharing the post on Twitter alongside the hashtag #ImWithHer in a show of support for Trump's opponent Hillary Clinton.
"The US President needs to understand & engage with wider world issues, not petty personal quarrels #ImWithHer."
