San Francisco (CNN) The fate of almost 3,500 people headed back to the United States remains a mystery as their cruise ship won't be allowed to dock anytime soon.

That's because the Grand Princess previously carried a passenger who has become the first person to die from coronavirus in California.

And dozens of passengers who were on the voyage with that man are still on the ship. At least two people who traveled with that passenger on the ship tested positive for the virus this week.

In this photo taken last month, the Grand Princess passes the Golden Gate Bridge in San Francisco.

The Grand Princess was on a 15-day trip and was scheduled to return Saturday. But the trip was cut short after news broke Wednesday of the California man's death.

The ship is now near the San Francisco coast but must remain at sea as it awaits testing for the virus from test kits delivered by helicopter Thursday.

Test results were expected Friday, said Mary Ellen Carroll, executive director of the San Francisco Department of Emergency Management.

She said 2,383 passengers and 1,100 crew members are aboard the ship. A total of 35 have shown flu-like symptoms during the course of the cruise, though many have recovered and are no longer showing symptoms.

Passenger Sharon Lane said she's worried about the elderly guests on board who may be more vulnerable to coronavirus.

"People are starting to get worried, and especially on this cruise," said Lane, who's from the United Kingdom. "On this cruise, it's mainly really elderly people."

Carroll said it's not clear when or where the ship will eventually dock, though San Francisco is a possibility.

"Public health officials have advised that no guests will be permitted to disembark until all (test) results have been received," Princess Cruises said in a statement.

But not all passengers will be tested.

"While there are no confirmed cases of COVID-19 currently on board, the CDC has identified groups of guests and crew who will be tested before arrival into San Francisco," Princess Cruises said in a statement.

"There are fewer than 100 guests and crew identified for testing, including all in-transit guests (guests who were on the previous Mexico voyage and remained onboard for the current Hawaii voyage), those guests and crew who have experienced influenza-like illness symptoms on this voyage, and guests currently under care for respiratory illness."

What we know about the man who died

The unidentified man was 71 and had underlying health conditions, Placer County health officials said.

He was likely exposed to the virus on a Grand Princess cruise from San Francisco to Mexico between February 11 and 21. His death was announced Wednesday.

The two people who tested positive for the virus who were on that cruise are in isolation rooms in a Santa Rosa, California, hospital, the Sonoma County Department of Health Services said Thursday.

Shortly after the Grand Princess finished its Mexico trip on February 21, it started another cruise to Hawaii.

Princess Cruises said 62 people on the current cruise were also on the previous voyage with the 71-year-old man.

California Gov. Gavin Newsom has declared a state of emergency, saying local health officials are working with their federal counterparts to trace people who had contact with the man who died.

"This emergency proclamation will help the state further prepare our communities and our health care system in the event it spreads more broadly," he said.

Princess Cruises said it has shared relevant travel and health data with the Centers for Disease Control and Prevention to help notify state and county health officials, who will follow up with anyone who may have been exposed to coronavirus.

How the testing will work

After the test kits are delivered to the ship by helicopter, a medical team on board will then administer the tests.

The test samples will then be sent by helicopter to a lab in Richmond, California, Princess Cruises said.

The cruise ship canceled its stop in Ensenada, Mexico, which was scheduled for Thursday, and headed back toward San Francisco instead.

Some passengers are confined to their rooms, but others aren't

The cruise line said federal health officials require anyone from the previous voyage to remain in their rooms until they've been cleared.

Passenger Cheri Breault Harris is confined to her room because she was a passenger on the previous voyage.

"They were going to examine us today, but that never happened," Harris said Wednesday. "I guess they are waiting for the CDC to say what to do after we get to (San Francisco)."

Harris said she's "not happy about being confined," but "luckily, my husband and I like each other."

"Spirits are as high as can be under the circumstances," she said. "We are blessed to be healthy, comfortable and well-fed."

In another part of the ship, Mark Pace and his wife, Beth, are celebrating her birthday on the cruise. They sailed from San Francisco to Hawaii, where they spent four days on several islands.

"We are a little nervous about it. We knew it was a possibility," Pace said. "We came prepared with two weeks of extra medication and my laptop so that I could work if we were confined."

The Florida couple said they were not confined to their rooms as of Wednesday night, but the captain on Thursday asked passengers to stay in their cabins until further notice, citing CDC recommendations, according to a recording sent to CNN by passenger Teresa Duncan Johnson.

Pace said they've noticed subtle changes on the cruise. They had to wash their hands and use hand sanitizer before getting a plate and silverware for the buffet.

"And crew handled everything," he said. "We were not allowed to serve ourselves."

In the recording Thursday, the captain also discussed CDC recommendations that "all guests practice social distancing, including staying six feet or two meters from other guests."

What we learned from the Diamond Princess debacle

It's not clear what will happen to the Grand Princess passengers after test results come back.

But another Princess Cruises ship, the Diamond Princess, was the site of a major coronavirus outbreak

After the first handful of cases were reported from the Diamond Princess, Japanese officials decided to quarantine the ship. Eventually, more than 700 people on board became infected with coronavirus

"The problem with the Diamond (Princess) cruise ship, as we've learned, was that when you quarantine people like that, with a few possible infected people, the likelihood of infecting many more people goes up," CNN Chief Medical Correspondent Dr. Sanjay Gupta said.

"Cruise ships are sort of a reservoir for these viruses, even outside of the coronavirus outbreak."

A top Japanese government adviser has said the quarantine of the Diamond Princess "may not have been perfect."

Dr. Norio Ohmagari, director of the Disease Control and Prevention Center at Japan's National Center for Global Health and Medicine, said infected crew members may have passed on infections to other crew members or guests.

But others said it's impossible to fully isolate staff members during a cruise ship quarantine.

"Unfortunately to maintain daily life of the more than 3,700 passenger cruise, we needed help, we needed support from cruise members to maintain the daily life," said Yosuke Kita of Japan's Ministry of Health, Labor and Welfare.

US coronavirus cases and deaths keep rising

That number includes at least 46 former passengers of the Diamond Princess cruise ship, the site of a recent coronavirus outbreak and quarantine.