"We attained a new record … in the daily median sea surface temperature of the Mediterranean: 28.71ºC," the institute said on Tuesday.
"The last record was in August 23, 2003, with a median value of 28.25ºC."
These findings are yet to be confirmed by Copernicus.
Copernicus recently said that at the beginning of June, global temperatures exceeded pre-industrial levels by more than 1.5ºC, which is the most ambitious cap for global warming in the 2015 Paris Agreement.
Such temperatures threaten marine life. During earlier heatwaves between 2015 and 2019, about 50 species including corals and molluscs, were eliminated.
Heatwave around the world - in pictures
The Mediterranean region, hit by record temperatures in July, has long been classified as a hotspot of climate change.
The UN's Intergovernmental Panel on Climate Change had warned that there was a drastic change in the marine ecosystems in the Mediterranean since the 1980s, with a decline in biodiversity and the arrival of invasive species.
IPCC experts have warned that more than 20 per cent of fish and invertebrates caught in the Mediterranean could disappear by 2060 if global warming exceeded the 1.5ºC target.