The giant panda cub was incubated by zookeepers because Mei Xiang had trouble nursing both cubs.
Staff swapped the small cub in for feeding with her mother on August 25 and saw the cub was struggling on August 26.
“When we realized the cub wasn’t going to make it, it was devastating,” zoo staff said.
The zoo said it was “prepared” to rear twin cubs and did everything it could to keep both of them alive.
Antibiotics and other liquids could not save the cub, who was having respiratory issues.
One zoo official said there had been some “misunderstanding” that Mei Xiang preferred one cub over another.
“We were optimistic, we think Mei Xiang was doing everything right, but we don’t know,” said Dr Donald Neiffer, chief veterinarian at the National Zoo.
“She was trying to balance and juggle two kids at the same time. There were days when she was a little less interested in taking a baby, but that occurred for both babies.”
No official cause of death has been named, but the zoo is running tests to figure it out.
The small cub weighed 86 grams when it was born, while the larger cub weighed 138 grams.
The 17-year-old Mei Xiang weighs 238 lbs (108kg).
Mei Xiang’s first cub, Tai Shan, was born in 2005 and returned to China in 2010. Her second cub, Bao Bao, just celebrated her second birthday.
Giant pandas are one of the most endangered species in the world and are notoriously hard to breed in captivity.
The National Zoo is one of only four zoos in the US to have pandas, which are on loan from China.
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