Two of the newborns - the world's second live-born set of octuplets - were initially put on ventilators, but their breathing tubes have been removed.
"Only three babies need some sort of oxygen through the nose right now but they are breathing on their own," Gupta said on "Good Morning America."
The mother, who was not identified, gave birth Monday to the six boys and two girls weighing between 1.8 pounds and 3.4 pounds. The eighth baby was a surprise to the parents and doctors who had been expecting only seven children.
"It is quite easy to miss a baby when you're anticipating seven," said Dr. Harold Henry, chief of maternal and fetal medicine and one of 46 doctors, nurses and assistants who delivered the children by Caesarean section.
Just five minutes after the first birth, the unexpected eighth baby came out at 10:48 a.m. "My eyes were wide," said Dr. Karen Maples, chief of the department of obstetrics and gynecology.
Doctors said they repeatedly conducted practice sessions in anticipation of the deliveries and were well prepared. Maples credited that with the ability to handle the unexpected eighth baby. "It was wonderful just knowing that our teamwork paid off," she said.
The babies - dubbed with the letters A-through-H - will probably remain in the hospital for at least two months and the mother should be released in a week, said Maples. The most encouraging news was that the smallest - Baby E, a boy weighing just 1 pound, 8 ounces - no longer needed a ventilator. Gupta described him as "very feisty" on Tuesday.
The doctors cautioned that there is still the possibility that one or more of the octuplets may need a breathing tube again, and more dangers await when they begin feeding.
The mother checked into the hospital in her 23rd week of pregnancy and gave birth to the premature babies seven weeks later. Hospital officials would not say whether she had used fertility drugs.
Their parents, Nkem Chukwu and Iyke Louis Udobi, told The Associated Press that they were delighted to hear another mother managed the same feat.
"It's a blessing, truly a blessing," Chukwu said. "We'll keep praying for them."
Dr. Richard Paulson, director of the fertility program at the University of Southern California, said the latest births likely resulted from the use of fertility drugs, and that the children could face serious health risks.
"It's a risky decision to try to have all eight babies," said Paulson, who had no role in the delivery. "I would not recommend it under any circumstances, but I respect a parent's decision."
The Bellflower medical center, located about 17 miles southeast of Los Angeles, has an advanced neonatal unit. The most infants previously delivered at the hospital was five, the Los Angeles Times said.
The birth took a lot out of more than just the mother. Maples, who helped deliver the brood, said that when she got home: "I was humbled, I was exhausted and I took a nap."