A dispute between two veterans in the Melbourne Press Club (MPC) has resulted in the resignation of three of its leadership team, leaving the club without a president, vice-president and chief executive.

Vice-president and co-host of ABC News Breakfast, Michael Rowland, MPC president Adele Ferguson, and CEO and former editor of the Canberra Times Mark Barker, all resigned abruptly on Tuesday and Wednesday.

Mr Rowland was reportedly the first to quit, saying he could not tolerate the ongoing dispute between Mr Baker and club member and former Age editor Michael Smith.