The Save Temple Cowley Pools group handed in a petition at a full meeting of the city council at the Town Hall on Monday.
It had more than 1,600 signatures and called on the authority to abandon its plans to close and demolish the facility.
Nigel Gibson, who is leading the campaign, said: “This petition asks the council to work with us to find a viable solution to keeping the Temple Cowley Pools & Fitness Centre open.
“The number of signatures, and the speed with which we collected them, demonstrates yet again the overwhelming support for the campaign from the general public.
“They simply can’t understand why such a popular centre, the most energy-efficient in Oxford and with the only publicly funded diving pool in the county, needs to be closed.”
Petitions which gather 1,500 signatures or more must be considered by a full meeting of the city council, according to the authority’s constitution.
This is the seventh petition which the campaign group has handed into the city council, which wants to replace Temple Cowley Pools with a new multi-million pound facility in Blackbird Leys.
Construction of the new pool is expected to be completed later this year.
The Temple Cowley site, which is earmarked for housing, has already been put on the market.