The CEO of Carnival, the world's biggest cruise company, says the huge demand for travel on its ships is outstripping supply

• Arnold Donald said Americans are desperate to return to Carnival Corp's cruises.
• "We have far more demand than we have ships available to supply right now," he told Fox Business.
• He added that the chance of a COVID-19 outbreak onboard is "very low," but can't be ruled out.

The CEO of Carnival Corp, the world's biggest cruise company, said that demand across its nine cruise lines is soaring and that Americans are raring to get back on the water.

"Honestly, people are champing at the bit to cruise again," Arnold Donald told Fox Business Friday.

Its first US cruise, the Vista, by Carnival Cruise Line, its biggest brand, is setting sail from Galveston to the western Caribbean on July 3.

Read more: Baby boomers, desperate to travel, are booking lavish getaways, month-long stays in villas, and exotic cruises

Donald said that people were confident in the safety of cruises as the vaccine rollout continues across the US, and that the shots were a "huge game-changer."

Bookings were "robust" and among the highest in the company's history, according to Donald.

He said: "We do not have an issue with being able to fill the ships. People are ready to sail. In fact, we have far more demand than we have ships available to supply right now."

In a second-quarter business update Thursday, the company said that booking volumes for future cruises were 45% higher than during the first quarter. It added that advance bookings for 2022 were already higher than in 2019, thanks to pent-up demand.

People are spending a lot of money on board, too. The CEO of Celebrity Cruises said travelers are eager to shell out extra cash on casinos, massages, and luxury meals.

Donald told Fox Business that some of Carnival's cruise lines, including Costa, had been sailing out of Europe during the pandemic. Many of these passengers were unvaccinated, but the company implemented universal testing, social distancing, mask-wearing, and enhanced medical screenings, he said.

There were less than 50 reported coronavirus cases out of around 400,000 guests on board, according to Donald, who added that guest satisfaction scores were "sky high."

Donald said that there would be some unvaccinated guests on its cruises in the US, but that these passengers would have to take regular COVID-19 tests and wear masks.

Celebrity Cruises last week unveiled new regulations subjecting unvaccinated passengers - or those unwilling to show proof of the vaccine - to onboard restrictions, extra COVID-19 tests, and additional costs.

But being fully vaccinated doesn't completely prevent the risk of catching or spreading COVID-19.

"If the virus is in the community on land ... then of course you can get it on board despite all the things we do," Donald told Fox Business.

"We can't guarantee there will never be a case on board, but the chance of an outbreak is very low," he added.

And on a "fully vaccinated" Royal Caribbean cruise sailing from the Bahamas, two passengers aboard tested positive for COVID-19. Both were under the age of 16, meaning they were exempted from the vaccine mandate.

Carnival said that at least 52% of its ship capacity would be sailing by the end of November, and expected to have its full fleet back in operation by spring 2022.

Donald told Fox Business that Carnival was selling or had sold 19 ships during the pandemic, reducing its total capacity by 13%, but that the company was buying more ships and would grow its capacity by around 2.5% through 2025.

He added that its newest ship, the Mardi Gras, was setting sail from Port Canaveral to the eastern and western Caribbean on July 31. Carnvial Corp said that the ship is the first in the world to have a rollercoaster on board, as well as the first in North America to be powered by liquefied natural gas.