The twin cubs born to the Smithsonian National Zoo's giant panda Mei Xiang were said Monday to be "doing well" after a night that had zookeepers on edge.

The cubs were born within five hours of each other on Saturday, triggering "pandamonium" at the much-visited zoo in the US capital.

"Our panda cubs are doing well, but the panda team had a challenging night," the zoo said in a brief statement.

Mei Xiang has been caring for the delicate and vulnerable newborns one at a time -- but when handlers tried late Sunday night to swap the cubs, she refused to let go of the one in her possession.

"Consequently, the panda team cared for the smaller cub throughout the night until 7:05 a.m. (1105 GMT) when they successfully swapped the cubs," it said.

Prior to the swap, the smaller cub was fed formula first by bottle, then by tube, with the latter procedure turning out to work "well and quickly."

"Our goal is for each cub to spend an equal amount of time with their mother," the National Zoo said.

"The newborn cubs are vulnerable and this first week is incredibly important and the risk remains high."

The first tiny cub -- pink, hairless and only about the size of an adult mouse -- was born at 5:35 p.m. (2135 GMT) Saturday and Mei Xiang reacted by tenderly picking it up.

Just when conservationists thought they had heard all the good news, the zoo tweeted: "We can confirm a second cub was born at 10:07. It appears healthy. #PandaStory."

While panda twins are not uncommon in the wild, they need intensive maternal care after birth, making survival precarious.

- Third set of US twins -

Mei Xiang's cubs are the third set of twins born in captivity in the United States. Only one set, born in 2013 at the Atlanta zoo, has survived.

Experts feel the best way to keep both cubs alive is to keep swapping them, so they each get quality time with their mother.

Still to be determined are the cubs' sex -- and father.

Mei Xiang, 17, was artificially inseminated in April with frozen semen from a male giant panda named Hui Hui from the China Conservation and Research Center for the Giant Panda in southwestern Sichuan province.

But she was also inseminated with fresh semen from the National Zoo's resident male giant panda Tian Tian. DNA tests will establish which is the father.

Mei Xiang had a cub in 2005 that was sent to China, and another, Bao Bao, is now two years old and lives with her in Washington.

Mei Xian has lost at least two other cubs -- one that was stillborn in 2013 and another that lived just six days in 2012.

This year, Mei Xiang exhibited signs of pregnancy in July that included sleeping more, eating less, building a nest and spending more time in her den.

She will spend almost all her time in her den for the next two weeks. The enclosure will be closed to ensure peace and quiet, though online "panda cams" provide a video stream of the creatures.

There are fewer than 2,000 pandas left in the wild, according to the World Wildlife Fund, as their habitats have been ravaged by development.