US distance swimmer Diana Nyad paddled onward Monday after an overnight storm threatened to sink the 62-year-old's fourth bid to swim from Cuba to Florida through jellyfish-infested waters.

Her crew said the skies had cleared by Monday morning and that she was on track to complete the 103-mile (166-kilometer) swim on Tuesday or Wednesday, having covered around a third of the distance in 42 hours in the water.

"Things couldn't look better right now. The sun is up," operations chief Mark Sollinger told NBC's "Today" show by satellite phone from one of the support yachts accompanying her.

"Her stroke looks good and we are moving in the right direction."

An overnight lightning storm hindered her progress, forcing her to tread water while the storm blew over, according to diananyad.com, the website documenting the endeavor.

"We had quite a night. The weather was really ugly. All crew members safe," Angie Sollinger, a member of the crew, wrote.

Nyad has been swimming steadily at 50 strokes per minute despite painful jellyfish stings on her lips, forehead, hands and neck.

Some jellyfish release a toxin that may affect a swimmer's performance, particularly in the case of multiple stings.

A build-up of such toxins in Nyad's body forced her to cut short a previous attempt to swim across the Florida Straits last year.

The athlete and author, who took to the water in Havana on Saturday, had aimed to make land in the Florida Keys on Tuesday, but Mark Sollinger said it was impossible to know the exact time or location of her arrival.

She is on her fourth attempt to cross the strait separating the two countries, which have been at odds for over five decades. Her most recent attempt was in September 2011.

Nyad's first attempt to make the crossing was in 1978, when she was 28 years old. Shoulder pain, asthma and ocean swells forced her to cut short another attempt in August 2011.

This time, Nyad has a specially designed bodysuit to protect her against jellyfish that she wears at night, when the creatures are most active and when the accompanying boats and kayaks switch on red lights to repel them.

The suit does not, however, prevent all stings, including by dangerous box jellyfish.

Nyad swims the backstroke at night to keep her face out of the water and avoid being stung, according to the crew, which works from five yachts and includes divers with shark experience as well as jellyfish experts.

The swimmer comes up to her Voyager escort boat, which she is not allowed to touch, around every 90 minutes to fuel up, sipping on a concoction of nutrients, electrolytes and calories through a CamelBak hydration pack.

Despite fatigue, she has not lost her appetite. In one of the meals, she had pasta and hot chocolate, the crew said. At other times, she has a spoonful of peanut butter, pasta or a bite of bread.

Stressing the immensity of the challenge, her team tweeted: "This swim is five English Channels, with sharks and box jellies added."

Nyad, who turns 63 on Wednesday, set an open sea record for both men and women by swimming from the Bahamas to the Florida Keys in 1979 -- a journey that is the same distance as the Cuba-Florida swim, but which she has described as far less dangerous.

And she set a record for circling the island of Manhattan at age 50, clocking in at seven hours and 57 minutes.

In July, British-Australian athlete Penny Palfrey, 49, failed to swim unassisted from Cuba to Florida and had to be plucked from the sea after nearly 42 hours in the water because of a strong current.