Councilmen Elzie Clements and Paul Moore voted to evict Browser.
"City Hall and city businesses are no place for animals," Clements said at the meeting.
The majority of residents addressing the council during the meeting spoke in support of Browser.
"This is not just a cat, it's like a family pet," former Councilman Alan Price said. He said supporters "will petition for an election if we need to -- we'll take this to November. I don't think that will be any problem."
Mayor Ron White, whose office makes him a a nonvoting council moderator, described Browser's eviction as petty retaliation for a city employee not being allowed to keep a puppy at City Hall.
"We've had that cat five years, and there's never been a question," the Fort Worth Star-Telegram newspaper quoted White as saying. "That cat doesn't have anything to do with whether somebody can have their puppy at City Hall. That cat doesn't hurt anybody... The council just went out and did this on their own because they don't like cats."
White said he will call for the council to reconsider its decision at the upcoming July 12 meeting.