Scott's team argued that the votes -- seven in favor of Scott and six in favor of Democratic incumbent U.S. Sen. Bill Nelson -- were not counted in last Saturday's reporting totals to the state because they failed to meet the submission deadline, and therefore shouldn't be included in Thursday afternoon's recount numbers.
However, Chief Judge Jack Tuter denied the request for an injunction.
Tuter cited that voters should not be disenfranchised solely on the failures of elections officials.
Tuter said the elections supervisor may segregate the ballots in the event of a legal challenge.
Unofficial election results show Scott leading Democratic incumbent U.S. Sen. Bill Nelson by just 0.14 percentage points.