The pace of testing in California had remained stubbornly low for weeks, but it appears to be on the rise. Still, the state, with twice the population of New York, has conducted far fewer tests for the virus. Limited testing in California may mean that the state may never get a clear handle on how many are infected.

In Louisiana, as testing ramped up, the number of cases surged. The state may be experiencing the world’s fastest rate of growth in new cases, which is largely attributed to Mardi Gras celebrations in New Orleans.

Washington State, where the first confirmed U.S. case was reported in January, faced a myriad of delays before large-scale testing began. Doctors in the state eventually began testing for the virus, without government approval, and found that it was already spreading locally.

New York has been testing aggressively. Health officials there say that a significant increase in testing has revealed the extent of the outbreak, especially in the New York City region, which is now the epicenter of the coronavirus pandemic .

Within the country, there is tremendous variation in the rate of testing among states. That’s partly because testing protocols and reporting procedures are often at the discretion of individual primary care physicians and public health departments at the state, county or city level.

But the United States, which has the most known coronavirus cases in the world, continues to lag in tests per capita, according to an analysis of estimates from the COVID Tracking Project . Both South Korea and Italy have much smaller populations than the U.S.

This week, the number of coronavirus tests in the United States surpassed those in South Korea and Italy — two countries that had been testing more aggressively.

About 65,000 coronavirus tests are being performed on Americans each day — a meteoric rise from just 10 days ago. But public health experts say that about 150,000 tests are needed every day, so that infected patients can be quickly identified and separated.

The United States cannot even test everyone who is sick because of a shortage of testing kits and personal protective equipment for health care workers. At the Elmhurst Hospital Center in Queens, the line of people waiting outside for a test forms as early as 6 a.m., with some staying until 5 p.m. Many go home without being tested.

Early flaws in the testing process — like not relying on the World Health Organization’s coronavirus test and problems with the test kits — cost the United States valuable time and has left the country with a haphazard testing process from coast to coast.

“If you’ve seen how one county does it, then you’ve seen how one county does it,” said Dr. Gary L. LeRoy, a family practitioner in Dayton, Ohio, who is the president of the American Academy of Family Physicians, which represents nearly 135,000 doctors and medical students nationwide.

Public health laboratories in all 50 states and Washington, D.C. are now testing for the coronavirus and many more labs are completing testing verification procedures outlined by the Federal Drug Administration. But some states are actively discouraging testing for anyone who is not showing symptoms, and a request from a doctor is no guarantee of a test, Dr. LeRoy said.

The state labs are largely being used for patients identified by the Centers for Disease Control and Prevention as high priority. This includes hospitalized patients with symptoms compatible with the coronavirus; those over 65; those with chronic medical conditions or compromised immune systems; those who show symptoms within 14 days of being in contact with a confirmed coronavirus patient; and those with a history of travel to China, Italy, Iran or South Korea.

Many states are also working with private companies like Quest Diagnostics and LabCorp for testing, both of which take up to five days to process tests, much longer than state labs. There are drive-through locations in every state, but they are few and far between, and many are limited to health care workers and first responders.

At a virtual town hall event for primary care doctors across the country on Wednesday night, many doctors were still asking about the availability of tests and how to get them, Dr. LeRoy said.

“It’s like sending the troops out there without ammunition and wondering why the battle is being lost,” he said. “We should have been the first to have the testing capability, the equipment and the knowledge.”