Health officials in California now say two people in that state died with the coronavirus weeks earlier than has previously been reported.

Officials in Santa Clara County said late on Tuesday that the people died in their homes on February 6 and February 17. Previously, the first death in the United States from the virus had been reported on February 29 in Kirkland, Washington.

The Medical Examiner-Coroner received confirmation on Tuesday that tissue samples sent to the US Centers for Disease Control and Prevention tested positive for the virus, officials said.

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Dr Sara Cody, the county's chief medical officer, told the New York Times that the two victims did not have any known travel history that would have exposed them to the virus, suggesting that they contracted the disease in the community.

Officials said the deaths indicated that the coronavirus may have been spreading in California much earlier than was previously known, and could dramatically shift the timeline of when and how the virus spread across the US.

"Each one of those deaths is probably the tip of an iceberg of unknown size," Cody told the Times. "It feels quite significant."

The announcement came after California Governor Gavin Newsom promised a "deep dive" update on Wednesday of the state's ability to test for the coronavirus and to track and isolate people who have it, one of the six indicators he says is key to lifting a "stay-at-home" order that has slowed the spread of the disease but forced millions of people to file for unemployment benefits.

"This will go to the obvious questions and queries that all of us are asking: When? ... When do you see a little bit of a release in the valve so that we can let out a little of this pressure," Newsom said on Tuesday, in what he says will be the first of regular weekly updates on the state's progress towards reopening.

Newsom says the state is testing an average of 14,500 people per day, up from just 2,000 tests per day at the beginning of April. Still, in a state of nearly 40 million people, that is not enough for public health officials to know for sure the reach of the highly contagious virus that is still causing outbreaks across the state in nursing homes and homeless shelters.

Newsom said he wants the state to test at least 25,000 people per day by the end of April.

Over the weekend, the California Department of Public Health issued new testing guidance that, for the first time, recommends testing for people in high-risk settings even if they do not have symptoms. The new advice is aimed at hospitals, jails and homeless shelters - three places where physical distancing is difficult.

California has more than 35,600 confirmed coronavirus cases and 1,300 deaths, according to data compiled by Johns Hopkins University.

California has been under a mandatory, statewide stay-at-home order for more than a month. Last week, Newsom said he will not consider loosening that order until hospitalisations, particularly those in intensive care units, flatten and start to decline for at least two weeks. On Tuesday, Newsom announced intensive care hospitalisations rose 3.8 percent.

Other indicators Newsom says he is monitoring include whether the state has adequate protective gear for healthcare workers, better treatment for the disease and expanded testing.

Newsom's news conference, scheduled for noon on Wednesday, will be watched closely by business groups who are clamouring to reopen so they can start paying their workers again.

"We just hope (on Wednesday) we might hear of some additional steps from the governor that small businesses will be able to take towards opening their doors and turning their lights on," said John Kabateck, state director of the National Federation of Independent Business.