Friends of the National Zoo Executive Director Clinton Fields said in a statement that the panda "suffered from the complications of kidney failure associated with advanced old age."
Veterinarians at the zoo say he had become increasingly weak and inactive, reports CBS News Correspondent Eric Engberg.
Zoo director Michael Robinson also mourned the panda's passing in a statement, saying, "Hsing-Hsing was an exceptionally good-natured animal that was loved by the National Zoo staff and millions of people around the world. His death is like the passing of a close friend."
Lisa Stevens, assistant curator of mammals at the zoo, told Early Show Co-Anchor Jane Clayson that pandas are "very special animals and very endearing and it's very easy to find a special place in our hearts."
More than Hsing-Hsing's memory will linger in Washington.
Visitors at the Smithsonian museum will continue to be able to visit Hsing-Hsing. The remains of the giant panda will be put on display early next year at the National Museum of Natural History, museum director Robert Fri announced Monday.
The panda will initially go on display in the museum's rotunda, and will move to the mammal hall when it reopens in 2003.
Hsing-Hsing came to the Washington Zoo with his mate Ling-Ling following President Nixon's historic trip to China in 1972. The pandas symbolized better relations between the two countries; so-called "panda diplomacy." Ling-Ling died in 1992 at the age of 23.
The panda pair were an instant hit at the zoo with more than 20,000 people visiting them on their first day, and millions more visiting them in the following years.
The pair mated many times but never produced any viable offspring. Their five cubs all died within four days.
Stevens explained why so few pandas born in captivity survive: "Giant pandas give birth to very small cubs that weigh only about four to five ounces and are fragile and dependent on maternal care."
Hsing-Hsing's death leaves the National Zoo without a panda. The zoo has negotiated with Chinese authorities about leasing pandas but has so far failed as the price of pandas escalates.
A spokesman for the zoo said he remained "optimistic" that the Chinese would accept the zoo's offer of $2.5 million for a 10-year loan of two pandas. He said the zoo's offer was more focused on its research and training capabilities rather than the cash offer.
Earlier this month, two giant panda cubs from China arrived at an Atlanta zoo. The two-year-old cubs, a male named Yang-Yang and a female named Lun-Lun, were brought to Atlanta on a 10-year loan at a cot of $1 million a year.
While Zoo Atlanta was able to fund that fee by raising its admission price to $12 from $10, the National Zoo has difficulty matching that size of offer since it has no admission fee.
The only other giant pandas in North America are three in San Diego.
Pandas are not that far from extinction: there are 200 in captivity and about 1,000 in the wild.
"We are conducting research and every bit of information that we can gather on these animals potentially will help us maintain a self-sustaining population in zoos and help us to apply it to managing animals in reserves in the wild," says Stevens.
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