In a paper to appear in a scientific journal this month, researchers said they came to this conclusion after watching how elephants on a Kenyan game reserve behaved towards a matriarch who fell ill and died.
The dying elephant - named Eleanor by the researchers from Britain and the US - was first assisted by an unrelated matriarch from another family.
At one point the helper, called Grace, was observed lifting the collapsed animal to her feet using her tusks.
When Eleanor fell again, Grace tried again to lift her up - this time without success.
Eleanor died where she fell, and was subsequently visited by elephants not only from her own family, but from four other families as well.
All the animals showed a distinct interest in the body, the scientists discovered, sniffing it with their trunks, hovering a foot over it, or nudging it with their tusks.
"It leads to the conclusion that elephants have a generalised response to suffering and death ... and that this is not restricted to kin," they wrote in a paper for the August issue of Applied Animal Behaviour Science.
The research was led by Iain Douglas-Hamilton, from the zoology department at Oxford University, who founded the charity Save the Elephants.
With colleagues from the University of California, his team monitored 50 animals on the Samburu National Reserve in northern Kenya, tracking them with GPS collars and taking automatically dated and timed photos.
"This behaviour in an animal species can be compared to human behaviour, and indicates that such feelings as compassion may not be restricted to our species alone"
Most animals, apart from humans, seem to show little interest in the dead bodies of their own species - but chimpanzees, dolphins and elephants are all known to show concern for the sick and dead, the scientists said.
"This behaviour in an animal species can be compared to human behaviour, and indicates that such feelings as compassion may not be restricted to our species alone," Douglas-Hamilton said.