Nyad was making her fifth attempt in 35 years to make the crossing. She set a record for the longest ocean swim without a shark cage or flippers, according to her crew.
Only 2 miles (3.2 km) short of reaching Key West 50 hours after she set off from Havana, Nyad paused briefly to thank her support team, treading water as she addressed the vessels bobbing in the sea around her, according to blog updates on her website.
"This is a lifelong dream of mine, and I'm very, very glad to be with you," she said. "So let's get going so we can have a whopping party," she added before resuming her journey.
The marathon swimmer has said this would be her final attempt, this time using a protective silicone mask to better protect her from potentially deadly box jellyfish that forced her to end one of two attempted crossings last year.
Her doctors aboard a support vessel said earlier on Monday that Nyad's tongue and lips were swollen, causing her speech to be slurred and raising concern about her breathing, the blog reported. Nyad was also "very cold" and had canceled scheduled feeding stops overnight "in the hopes that swimming would keep her warm."
Nyad said at the outset that the custom-made mask slows her and makes it more difficult to breathe. Officials initially estimated it could take up to three days to complete the swim, but Nyad was benefiting from a favorable current, her crew members said.
The treacherous Florida Straits has been conquered only once, by Australian Susie Maroney, who used a protective cage at age 22 during a 1997 swim. The cage glided on ocean currents and enabled Maroney to make the journey in just 25 hours.
Australian endurance swimmer Chloe McCardel abandoned her quest in June to make the crossing after she was severely stung by a jellyfish 11 hours into her attempt.
Nyad's fifth attempt to make the crossing comes 35 years after her first attempt at age 28, in 1978, when she gave up after covering 76 miles in 42 hours, that time with the aid of a shark cage.
Nyad departed on Saturday morning accompanied by five support boats that also provide her with food and water.
As night fell on Sunday, Nyad put on a jellyfish-protection suit, the website said. She did not immediately use her protective mask. Instead, the exposed parts of her face were slathered with a special protective cream dubbed "Sting Stopper," it said.
At one point on Sunday, Nyad floated on her back kicking and led a crew of 35 people keeping her on course through the strong Gulf Stream current in singing "Happy Birthday" to a crew member.
"Diana is feeling strong and very coherent," an earlier update read. "She is joking for the first time all day. The only concern is that she is throwing up everything she eats."
Earlier Sunday, Nyad was stopping every 40 minutes to eat, taking several bites of scrambled eggs and pasta, the blog said.
Her previous long-distance accomplishments include swimming around the island of Manhattan in 1975 and a swim from the Bahamas to Florida in 1979.
(Writing by David Adams and Kevin Gray; Additional reporting by Marc Frank in Havana; Editing by Marguerita Choy and Cynthia Osterman)