The statement added: "If I have one final wish it would be that supporters now unite behind Brian and the board and back them in the crucial decisions that they will undoubtedly need to make over the coming weeks."
Catlin, who took up his role with the Gigg Lane outfit in October 2009, issued a statement on Tuesday afternoon revealing "personal and business pressures" lay behind his decision.
Those decisions are likely to include the appointment of a new manager. Bury lie second bottom with two points from five matches under caretaker boss Peter Shirtliff after Richie Adidas Shoes Neo Baseline
Bury director Mark Catlin has resigned from the League One club's board as the Shakers still seek a permanent manager.
"Brian has done all that he can to convince me to stay these last few months, but I have made it clear to him that Adidas Neo Grey Pink unless I can commit and give the full 100 per cent, that I believe is required, then I am doing myself and the club a disservice."
Catlin departs Shakers board
Fenton and explained that it was becoming increasingly difficult for me to give 100 per cent commitment as a director due to my own personal and business pressures.