The team that wrote the study, including lead author Professor Roberto Orosei, have ruled out any other causes for the brightness.
Whatever the outcome, the researchers say it would take years to verify whether something is living in the reservoir.
What is believed to be liquid water is sitting below Mars' southern polar ice cap and is described as a "well-defined, 20-kilometer-wide zone".
The presence of liquid water on Mars has always been suspected but thus far evidence from MARSIS remained inconclusive.
However, the planet's climate has since cooled due to its thin atmosphere, leaving most of its water locked up in ice.
Scientists have long said Mars could potentially host life, and finding liquid water on the Red Planet is seen as one of the most important aspects of that search for extraterrestrial life. It stretched about 12.5 miles across and looked very similar to lakes that are found beneath Greenland and Antarctic ice sheets on Earth.
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Almost 4.5 billion years ago, Mars had six and a half times as much water as it does now and a thicker atmosphere. Because it is salty, or briny, it remains in its liquid form and does not freeze.
For the first time ever, scientists believe they've discovered a significant body of liquid water on Mars.
"We found that any other explanation for these very strong echoes was not really tenable in light of the evidence that we had available", he said.
There have been previous signs of liquid and water activity on Martian slopes, but never before a "stable body" - which strengthens the notion of alien life inhabiting the planet.
"All the technology to drill through this ice to the lake doesn't exist yet so it will probably take at least another 25 years before we will be examining this".
"It's an exciting discovery, if it's true", said Tanya Harrison, Professional Martian and Director of Research for Arizona State University's Space Technology and Science Initiative, who was not involved in this discovery, "since we know that life can survive in subglacial lakes, and brine pockets inside glaciers, here on Earth".
The researchers noted that together, with the pressure of the, this lowers the melting point, allowing the lake to remain liquid, as happens on Earth.
Last week data were released revealing that there are organic molecules on Mars. The announcement is likely to get scientists thinking about how to use existing instruments orbiting Mars to give this region a more careful examination.