It also uncovered details of an affair between acting Immigration Minister Alan Tudge and his former staffer Rachelle Miller, who has since made a formal bullying complaint against Mr Tudge.
Mr Fletcher on Tuesday posted a copy of his letter to Ms Buttrose - which makes repeated references the ABC’s editorial policies - to Twitter, but disabled the comment function on the post.
He accused the program of showing anti-Liberal Party sentiment because it did not investigate any actions of Labor or Greens politicians. Labor and the Greens are not in government.
“Why should an objective observer not conclude that the program evidenced clear bias against the Liberal Party, with this bias evident in the choice of persons interviewed, the making of specific allegations in the face of clear factual denials, and the fact that the program failed to investigate or report on conduct engaged in by Labor, Greens or independent politicians?” Mr Fletcher wrote.
Mr Fletcher also questioned why Four Corners relied on statements from Greens Senator Sarah Hanson-Young to back up allegations against Mr Porter and why it didn't disclose the "strong political affiliations" of others interviewed for the episode.
The ABC's managing director David Anderson was called to a Senate inquiry before the program was aired to confirm he and Ms Buttrose had already seen it and thought it was appropriate.
Mr Fletcher asked Ms Buttrose why the personal lives of politicians are newsworthy.
"Why, in the judgment of the board, are the personal lives of politicians newsworthy?" Mr Fletcher wrote.
"Why in the judgment of the board is the existence of a consensual relationship between a politician and a staff member that occurred prior to the introduction of the ministerial code considered newsworthy?"
The program pointed out Mr Tudge framed himself as a family man to justify voting against marriage equality, painting him as a hypocrite for having an affair.
The journalists involved in the program have vehemently defended the program's newsworthiness and revealed the government's attempts to stop the public from seeing it.
Mr Porter swiftly rejected the way he was depicted in the episode after it aired and said he was considering legal action.
Mr Tudge issued a brief statement after the program aired.
"I regret my actions immensely and the hurt it caused my family. I also regret the hurt that Ms Miller has experienced," he said.
Scott Morrison has refused to take action against either minister, saying neither had breached ministerial standards while he was prime minister.
Allegations against the two ministers pre-dated changes to the ministerial code of conduct, which banned sexual relations with staff.
The ABC has been contacted for comment.