California officials said this week that they had bolstered efforts to confront the growing threat of the coronavirus, declaring that they were prepared and pursuing aggressive measures to thwart its spread.

Gov. Gavin Newsom said on Thursday that the state had pushed for improved and expanded testing, urging federal officials to alter a testing protocol that he considered “inadequate” to address the situation California faces. He also said officials were actively monitoring people who might have come into contact with the pathogen.

California has had more coronavirus cases than any other state and has also been the nucleus of quarantine efforts in the United States. The sense of concern became more heightened after officials confirmed what is believed to be the first documented case of community transmission, in Solano County.

The governor sought to strike a delicate note by quelling fears over the virus while acknowledging the seriousness of the situation. He told residents that the overall number of cases remained low and that the state government was well positioned to keep it that way.

“We have been in constant contact with federal agencies,” Mr. Newsom, a Democrat, said in a news conference on Thursday. “We have history and expertise in this space. We are not overreacting, but nor are we underreacting to the understandable anxiety that many people have as it relates to this novel virus.”

Mr. Newsom has resisted declaring a state of emergency, a step taken by some local officials largely in an effort to muster public health resources. But there are worries about the economic fallout, with events having already been changed or canceled. Both Facebook and Microsoft said they were pulling out of conferences scheduled for March and May.

How many people are infected in California?

Thirty-three people have tested positive for the virus in California, said Dr. Sonia Angell, the director of the California Department of Public Health. Out of that group, 24 were from repatriation flights, seven were related to the patients’ travel and one had contracted it from an infected spouse. The most recent case was the one involving community transmission, which was reported in Solano County.

How many people are being tracked?

Mr. Newsom said five people had moved out of the state after testing positive. In addition, at least 8,400 people who have returned from overseas are being monitored in 49 jurisdictions.

What makes Solano County a focus of concern?

One confirmed coronavirus case that cropped up in Solano County, between San Francisco and Sacramento, is especially worrisome to health officials. The patient had not had contact with anyone known to be infected, and had not traveled recently to a country where the virus is known to be in circulation.

The Centers for Disease Control and Prevention said it was the first such case reported in the United States, and it raised the possibility that someone who is asymptomatic may be carrying the virus and infecting others without knowing it.

The patient, a woman, became ill and was first treated in a hospital in Vacaville, then transferred to the UC Davis Medical Center. Doctors there suspected coronavirus and requested a test. But the C.D.C. did not perform the test for days, because it was restricting testing to sick people known to have been exposed to the virus. The day after her case was confirmed, the C.D.C. broadened its criteria to allow testing of people like her who appear to be ill from coronavirus but have no known point of exposure.

Solano County is also the location of Travis Air Force Base, where many Americans who were infected in Asia have been quarantined.

A government whistle-blower has filed a complaint saying that the federal health officials sent to interact with quarantined people at the base were not given proper training or protective gear, were not monitored or tested, and were allowed to move freely around and off the base — practices that potentially could have spread the virus into the community. The Department of Health and Human Services said it was looking into the complaint.

Similar things may have happened at Marine Corps Air Station Miramar near San Diego, another base where American coronavirus evacuees from Asia were taken to be quarantined, according to a person with direct knowledge of the efforts there.

How is the state responding?

California officials said on Thursday that the C.D.C. had promised to vastly expand the state’s ability to test patients for the coronavirus. Mr. Newsom repeatedly said the previous system had been “inadequate” to keep the virus from spreading.

Mr. Newsom said the director of the C.D.C. had promised him that physicians would have a much greater ability to test patients who were showing symptoms of the infection, changes the governor said “can’t happen soon enough.”

“Testing protocols have been a point of frustration for many of us,” Mr. Newsom said, referring to health officials in California and governors of other states. State officials said California had just 200 testing kits left.

Even as the governor resisted declaring a statewide emergency, officials in San Francisco and Orange County announced they were taking that step. But officials in both places stressed that the move was less an acknowledgment of an active crisis and more about mobilizing the resources to prevent one.

“This declaration of emergency is all about preparedness,” San Francisco’s mayor, London Breed, told reporters on Wednesday.

Nichole Quick, the health officer for Orange County, said the formal declaration there would enable local officials to be “more nimble and flexible” in their response.

“This is a rapidly evolving situation,” Ms. Quick said on Wednesday, according to The Orange County Register, which reported that there had been one confirmed case of the virus in the county.

Can a state force a city to house patients?

State officials planned to move people infected with the virus to a state-owned facility in Costa Mesa, a city of more than 100,000 in Orange County. But city leaders are fighting to keep them out.

The authorities in California selected the site after the Defense Department informed them that patients who tested positive for the virus could no longer stay at Travis Air Force Base.

Federal officials had planned to move the patients to a government facility in Alabama, court documents said, but officials in California thought that moving the group, most of them said to be residents of the state, would be detrimental to their health and well-being.

Instead, state officials said the people would be moved from the base in Solano County to the facility in Southern California, where they would remain in isolation while recovering.

But the decision touched off a legal fight with Costa Mesa. A federal judge issued a temporary restraining order to stop the move. The judge said she would reconsider the issue after state and federal authorities provide more details about how they plan to protect the health of the community, as well as the people with the coronavirus. The judge set a hearing for March 2.

“This is a new one in terms of claiming a right not to have infectious disease introduced into your community,” said Polly Price, a professor of law and global public health at Emory University. Although cities and towns once claimed “an absolute right” to guard against disease, she said, state-level control over isolation and quarantine has been the norm for more than a century.

What has life been like for evacuees on the military bases?

Blair Zong, 33, was among hundreds of Americans who were evacuated on flights arranged by the U.S. government and have had to wait through mandatory 14-day quarantines on military bases.

Ms. Zong, who lives in San Jose, Calif., was visiting her mother and grandparents in Wuhan, China, where she grew up, when the coronavirus outbreak became an epidemic.

She agreed to keep a daily journal of her time in quarantine at Marine Corps Air Station Miramar in San Diego.

Reporting was contributed by Patrick J. Lyons, Sean Plambeck, Roni Caryn Rabin, Farah Stockman, Louis Keene, Emily Cochrane, Margot Sanger-Katz and Noah Weiland.