“So, if you think you might have Covid-19, want the reassurance that you don’t or you’ve been around people that you have seen with symptoms, get a test,” the mayor said. “We can do it.”

Gov. Gavin Newsom of California had outlined this week how the state might gradually reopen, and Mr. Garcetti said the availability of testing was a “really important step to prepare for other steps forward.”

It is unclear how many people will sign up to be tested or how long they will have to wait. Just over six million people have been tested in the United States, including about 603,000 in California, according to Johns Hopkins University data. More than 10 million people live in Los Angeles County, according to the Census Bureau.

In response to a reporter’s question about how the city would manage to test so many people, Mr. Garcetti said the city had tests left over each day and was confident in its ability to test any resident who wanted it, including those who want to get tested multiple times over the course of several weeks or months.

Mr. Garcetti said the testing would be carried out at 34 sites in the city that have the capacity to test at least 18,000 people each day. At least 140,000 people have been tested at those sites in the past month, he said.

About 22,485 people in Los Angeles County have tested positive for the virus, and the death toll there has risen to 1,056.