Marseille had hit out at their fans' representatives earlier this week after they allegedly threatened the club's management and pressured them to resign during a meeting held on Monday, saying they had received "personal threats".
Marseille are third in Ligue 1 after five games but they failed to qualify for the Champions League group stage this season when they were knocked out in the third qualifying round by Panathinaikos on penalties.
"I had a very long conversation with owner Frank McCourt and the supervisory board, who showed me their unconditional support... Today I'm speaking from the heart, but also as president of Olympique de Marseille," Longoria told reporters.
"I'm not going to go back over what happened on Monday, it's simply unacceptable.
"Throughout the week, I've been touched by the outpouring of support, the expressions of confidence and affection from all sides - players, employees, supporters, political and institutional players -- all those who have understood the need for change."
Longoria also said he has asked his lawyers to file a complaint following the meeting with the fan groups, adding that they must put an end to such behaviour and ensure such situations are not repeated in the future.
Due to the tensions with the fans, the club said they were forced to part ways with head coach Marcelino (58), who was in charge for only seven games having taken over in the close season.
"In life, I'm a person of values, of very strong convictions. I can't just denounce a situation, I have to get to the bottom of things. This is not about fuelling a conflict," he added.
"I am aware that I am going to begin the most difficult period of my mandate as president, with many potentially unpleasant situations. But I remain firm and determined to continue my mission.
"This is a new stage in this period of transformation. To accomplish this, I need the support of all those who love the club. We must emerge bigger and put an end to the practices I have denounced."