Despite speculation about his future the 67-year-old French coach finally signed a new two-year contract after the end of last season in which Arsenal finished fifth.
"I want the atmosphere to be united," Gazidis said at a fans event on Friday. "It has been a struggle because we haven't had that.
"There has been disagreement. There has been a lack of unity and dissatisfaction. The board knows that.
"I beg you, please come together and give our manager and this team support."
Gazidis, whose own relationship with Wenger was reported to have become strained last season, promised fans that the club were aiming to secure 'top-quality' new faces.
However, they have seen a big money bid for French international striker Alexandre Lacazette rejected by Lyon and their only signing so far has been Bosnian international defender Sead Kolasinac on a free transfer from Bundesliga outfit Schalke 04.
They also face a battle to retain their star player Chilean Alexis Sanchez -- who inspired them to salvaging their season with victory in the FA Cup over champions Chelsea -- as he has been increasingly linked with a move to Manchester City.
"We're looking for top-quality players," said Gazidis.
"We've got three times as many scouts as we had four years ago. I believe that to be a world-class football club, you've got to be world class off the pitch."