Social care chiefs have been urged to build a new care home on another site in Anstruther to avoid the loss of part of Bankie Park.
Land at Skeith would be more suitable for the £6 million facility, according to the Royal Burgh of Kilrenny, Anstruther and Cellardyke Community Council.
A proposal to erect the new building on part of the park has prompted outrage in the town and a campaign has been launched to protect the treasured green space.
Fife Health and Social Care Partnership and Fife Council are consulting on the plan to replace adjacent Ladywalk House care home.
But the community council has pressed them to reconsider other potential locations, in particular that next to Skeith Health Centre.
In its submission, it said: “The community council fully supports the building of a replacement care home in Anstruther but is concerned that the strength of feeling about the Bankie Park site will make it very difficult for Fife Council to pursue this through the planning process.
“We therefore urge Fife Health and Social Care Partnership to actively re-evaluate the other sites suggested, especially Skeith Health Centre, and explore any other possible sites that may be available in the area.”
It said the Skeith site would be widely supported in the community.
Buying the land, which it believed would cost around £150,000, could be funding through the sale of Ladywalk House, it said.
Fife Health and Social Care Partnership said at the launch of the consultation that it had identified a preferred site but plans were at a very early stage.
It said replacement of Ladywalk House was necessary due to its age and condition.
Construction would be on the part of Bankie Park adjacent to Ladywalk House and away from the play area, it said, with the Ladywalk House site returned to park land on a like-for-like basis.
The consultation, initially due to conclude at the end of July, has been extended until the end of August.
