The two-minute, 30-second video with Walt Ekard was posted on the city's website on Thursday.
"Our city is going through a rough time right now, and reading the news every day can be demoralizing," Ekard said. "But we have an important job to do, and we need to be focused on the task at hand."
Ekard, who retired last year as the County of San Diego's chief administrative officer, joined Filner's administration last week as part of a management shake-up that followed allegations that the mayor has sexually harassed women.
He was also accused of berating a top official in the City Attorney's Office and ordering police to remove him from a closed session meeting of the City Council.
The Filner administration is also under investigation for a policy change on a Kearny Mesa apartment complex after the developer donated $100,000 to the city, according to published reports. The money was later returned.
Ekard, who was widely praised during his tenure as the county's CAO, previously served Filner in an advisory role. His hiring has been viewed as an attempt by the mayor to steady the ship.
"Over the next few months, we'll be focusing on continuing to move this city forward, in spite of whatever distractions there might be," Ekard said.
He promised to improve internal communications so that "all employees have an opportunity to know where we are and where we're going as an organization." The Filner administration's communications efforts have been criticized since he took office.