The Centers for Disease Control and Prevention on Thursday raised its Covid-19 warning level for cruise ships to 4, the highest, and issued a blunt warning: “Avoid cruise travel regardless of vaccination status.”

The move came as the number of outbreaks on ships has grown in recent weeks, causing some ports to turn away ships. Last week, dozens of people on a Royal Caribbean International ship tested positive after it set sail from Fort Lauderdale, Fla., and a Carnival Cruise Line ship returned to Miami on Sunday after positive tests among “a small number on board.”

Calling the C.D.C.’s decision “perplexing,” the cruise industry’s trade group, Cruise Lines International Association, said in a statement that the number of cases onboard made up a very slim minority of the total population and that “the majority of cases were asymptomatic or mild in nature, posing little to no burden on medical resources onboard or onshore.”

Before the C.D.C.’s warning on Thursday, Royal Caribbean Group, one of the biggest cruise companies, said its ships had carried 1.1 million guests since it had restarted U.S. operations in June, with 1,745 people testing positive. While the majority of passengers had mild or no symptoms, 41 people were hospitalized.

“Omicron is having a big short-term impact on everyone, but many observers see this as a major step towards Covid-19 becoming endemic rather than epidemic,” said Richard D. Fain, chairman and chief executive of Royal Caribbean Cruises.

Despite the increase in cruise ship cases, Mexico’s government announced this week that it would let cruise ships dock at its ports even if passengers have tested positive for the coronavirus, and also allow asymptomatic travelers to disembark on its shores.

The announcement came after two cruise ships with Covid outbreaks were refused permission by the authorities in Jalisco State in the last week to let passengers or crew disembark at Puerto Vallarta, a popular tourist destination on Mexico’s Pacific coast.

“Our country maintains its policy of solidarity and fraternity, as well as the principle of non-discrimination towards all people,” the government said in a statement. “The health and tourism authorities remain attentive to provide the necessary medical assistance to those who visit us.”

The coronavirus wreaked havoc on the cruise industry in the early stages of the pandemic, infecting hundreds of cruise passengers and workers and requiring the sector to shut down for 18 months. To begin sailing, cruise ships had to agree to the C.D.C.’s Conditional Sailing Order, which is valid until Jan. 15.

On most cruises out of U.S. ports, almost all crew members and adult passengers are vaccinated and masks are required indoors except for when passengers are eating or drinking.

Among the safety measures the order requires — beyond submitting the daily number of coronavirus cases — is a prevention and control plan for each cruise ship.

Most cruise companies do not publicly announce the number of coronavirus cases identified during sailings, but all cruise ships operating to and from U.S. ports must submit daily numbers to the C.D.C., which uses a color-coded system to inform the public whether the number of cases is above or below the agency’s threshold for an investigation.

Currently 88 cruise ships are being monitored by the C.D.C. because of reported coronavirus cases onboard. The agency does not publicly specify the number of cases on each ship.