The Rossoneri are 11th in Serie A with 10 points after 12 games, the club's worst start to a campaign for 32 years, and the Italian media had reported that Galliani's position was in question.
Club director Barbara Berlusconi, daughter of club president Sylvio, was said to be considering dismissing Galliani but has denied the rumours.
Berlusconi says she spoke to her father about a "change of business philosophy at Milan," leading to Galliani making a public response.
"It is a difficult time because the results don't seem to be coming. We will move on and hope that things get better," said Galliani, who has been involved with AC since the mid-1980s.
"Today I only intend to speak about footballing issues, I have no intention about commenting on anything else; there is no comment.
"The chief executive is responsible for everything - transfer policy, revenue, accounts, everything. I have spoken a lot to the president, including last night.
"There have been other difficult times in 28 years. Sport is a cycle. I want to remind people that we come off the back of a Scudetto, a second place and last year we finished third, and we are the only Italian club side that has been present in the Champions League for the past five consecutive seasons. Sport is made up of these cycles that alternate."
Galliani also backed under-fire coach Massimiliano Allegri following the 2-0 defeat by Fiorentina on Saturday, Milan's fifth defeat in the league this season.
"There is absolute confidence in Allegri," he added. "Naturally, all coaches are dependent on results. If a coach constantly loses, then obviously that isn't good enough, but I don't think that this will be the case for us."
Club vice-president Galliani also reiterated how important he feels Mario Balotelli is to the club. Reports had linked the enigmatic striker, who joined Milan from Manchester City in January, with a move to Chelsea but Galliani feels the 23-year-old will be key to improving fortunes.
He added: "He came in February and in 13 league games - at the time he couldn't play in the Champions League - he scored 12 goals. Without Balotelli, we would never have even qualified for the Champions League.
"His first season was fantastic, and now we will wait and see how his second season goes. Is he indispensable to the side? Absolutely."