Wikie, a 16-year-old female orca living in a French marine theme park, has been recorded copying words such as “hello” and “Amy”, as well as counting “one, two, three”.
The sounds emerge as squawks, whistles or raspberries but most are clear enough to understand.
The scientist who led the study said it was conceivable that basic “conversations” with her may one day be possible.
Dr Jose Abramson, from Complutense de Madrid University in Spain, said: “It has been done before with a famous grey parrot and dolphins using American sign language; sentences like ‘bring me this object’ or ‘put this object above or below the other’.
“But you have to be careful about imposing our human concepts on animals.
“We will gain more if we try to understand the natural way each species communicates in its own environment than if we try to teach a human language.”
Killer whales in the wild and in captivity have previously been observed copying dolphin calls and the barks of sea lions.
Wild killer whales are also known to live in groups with unique vocal “dialects” – learned sounds used for communication that are kept within a particular population and passed to future generations.
But Wikie is believed to be the first member of her species to mimic human speech.
The experiments, carried out at her home at Marineland Aquarium two years ago, are reported in the journal Proceedings of the Royal Society B.
Wikie was taught to copy novel sounds and words from both another killer whale – her own three-year-old calf, Moana – and by humans.
She “spoke” while partially immersed in water with her blowhole exposed to the air.
The human words and phrases she attempted to copy included “ah ah”, “hello”, “bye bye”, “Amy”, “one two” and “one two three”.
Speech recognition software was used to test how well she performed.
Dr Abramson said: “In human intelligence, cultural and social learning aspects are very important.
“We can say that killer whales and other cetaceans have a highly developed social intelligence.”
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Marineland, located in the Antibes resort in southern France, faced criticism in 2015 after one its killer whales died during flooding.
Last year the company vowed to fight a ban on breeding killer whales and dolphins in captivity, claiming it would harm its animals.