They can weigh up to 13kg at certain times of the year and are very fast moving in the water.
"Both species are very fast swimming and agile animals," says Dr Karine Delord of the French National Centre for Scientific Research, who observed the behaviour.
Usually, the penguins are predated upon by much larger leopard seals and orcas.
Fur seals are also known to prey on king penguins on the shore, a behaviour filmed by the BBC Planet Earth Series.
"But our observations add strength to the unique similar predation in the water," says Dr Delord.
She and her colleagues Dr Yohan Charbonnier and Dr Jean-Baptiste Thiebot were studying the conservation of penguins, sooty albatrosses and giant petrels around Possession Island, one of five small islands that make up the Crozet archipelago in the southern Indian Ocean.
While located high up on top of a nearby cliff, they witnessed fur seals predating on king penguins below them in the sea on 17 occasions during five days.
Sometimes the penguins escape injured, sometimes they do not
The longest chase took five hours, when one male fur seal successively attacked at least ten king penguins.
Though all were injured, each made it to the shore.
Later the researchers witnessed a fur seal killing and eating a king penguin at sea.
"We found that predation on king penguins by Antarctic fur seals is more common and widespread than previously reported," says Dr Delord.
"It is too early to assess the impact of such behaviour because our observations need to be quantified on a longer period of time and other colonies of king penguins."
However, as seal numbers increase in the area, they could start to have a greater impact on small populations of king penguins.
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