Scientists at NASA in the United States and the UK's Open University found traces of carbon in tiny tubes inside the rock that resemble material found in fractures etched by microbes in volcanic glass from the Earth's ocean floor.
Even if the carbon was not the product of Martian microbes, its discovery, if confirmed, means that the two basic building blocks for life - carbon and water - are, or were, present on the planet. Carbon has been found in meteorites originating from Mars before, but sceptics have dismissed these, as it could not be proven that the Martian material was not contaminated with carbon from Earth.
However, this meteorite, which landed in the Egyptian town of Nakhla in 1911, killing a dog, was almost completely encased in a crust of material, which it is thought will have prevented earthly contaminants from getting in.
Professor Colin Pillinger, of the Open University, told The Scotsman: "These are very interesting results. We are very confident this stuff is carbon, and that is interesting because no carbon has ever been found on Mars, apart from in the atmosphere.
"For life to exist, you obviously have to have carbon fixed into organic matter. We cannot say we've found living matter, but we have found organic matter in meteorites. This is the best evidence we have yet of indigenous [Martian] carbon."
He said further tests had to be carried out to show that the carbon was Martian. The meteorite is known to come from Mars because tiny air bubbles inside the rock have been matched to the planet's atmosphere, which was measured by a probe.
Prof Pillinger, the scientist behind the failed Beagle 2 mission to Mars, said the meteorite was a "totally unique sample", adding that its thick crust "would have kept contamination out".
Dr Kathie Thomas-Keprta, of NASA's Johnson Space Centre, who co-authored a paper on the meteor to be presented at the Lunar and Planetary Science Conference in Houston, Texas, next month, said: "Our results strongly support an interpretation that this carbon is indigenous to Mars and is very unlikely to be a terrestrial contaminant."
However, Dr Caroline Smith, meteorite curator at London's Natural History Museum, where the Nakhla rock was kept, said more work was needed before any conclusions could be made.