Fungus-like life forms have been found in rocks dating back 2.4 billion years.
The fossils, drilled from rocks that were once beneath the seafloor, resemble living fungi.
Scientists say the discovery could push back the date for the oldest fungi by one to two billion years.
The find suggests that fungi arose not on land but in the deep sea. If not a fungus, the organism could be from an extinct branch of life that has not been described before.
Prof Stefan Bengtson of the Swedish Museum of Natural History led the research team.
He said, in the past, scientists may have been looking in the wrong place for the oldest fossil fungi - on land or in shallow seas rather than in the deep sea.
"The deep biosphere (where the fossils were found) represents a significant portion of the Earth, but we know very little about its biology and even less about its evolutionary history," Prof Bengtson told BBC News.
The fossils are almost indistinguishable from those found in similar environments on land, although they are much older.
They are made up of jumbles of tangled threads some hundredths of a millimetre thick.
Scientists have already discovered such structures - known as mycelia - in similar rocks of a much younger age and identified them as fungi.
There is a "clear possibility" that they are the world's oldest fossil fungi - twice as old as generally accepted in the fossil record, Prof Bengtson said.
If they are not fungi, they are probably an extinct branch of eukaryotes "or even giant prokaryotes", he added.
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