That's despite Mayor London Breed's dire prediction Wednesday on ABC7 News that her city could run out of the COVID-19 vaccine as soon as Thursday.
"We anticipate everything we have in our possession will be gone by Thursday," Breed said earlier this week.
RELATED: CA says its safe to resume Moderna vaccine use
Good news came Wednesday night when California cleared the Moderna vaccine for use after concerns about allergic reactions from the vaccine.
This frees up hundreds of vaccines for San Francisco to distribute this week, and another 10,000 doses next week.
"While that's better than what we received last week it is not sufficient to meet the demand and certainly not to meet our goal of vaccinating 10,000 a day."
A vaccine site at City College of San Francisco is having a soft opening Friday, where 500 vaccines will be distributed, but on an appointment-only basis.
CALCULATOR: Find out how many people may get a COVID-19 vaccine before you
"Those appointments are already filled so we do ask people not to show up there. We will not have additional vaccine to give," said Andrea Tenner with the San Francisco COVID-19 Command Center.
The larger goal is to vaccinate 10,000 people per day, through June.
If you add up the city's batch of vaccines with those from private providers, only half of the 200,000 people in the state's Tier 1A will have been vaccinated.
"All of those people need two shots, so to even deal with the 1A tier, we need about 400,000 vaccines, so we're nowhere near close to where we need to be," said Mayor London Breed.
VIDEO: 500 vaccines to be distributed on Friday at San Francisco City College
There is so much frustration with the state's phased distribution, that there are reports Thursday night that Sacramento may be considering doing away with phase Tier 1A and may instead consider a person's age as the primary factor.
If that's so, San Francisco says it will follow any new state guidance.
So far there are reports that some of the vaccine is being diverted to Southern California because of its surge in cases.
Mayor Breed also points out that when it comes to vaccinating people, San Francisco is somewhat unique when compared to other Bay Area cities.
"Many of the people who work for the city and county of San Francisco also live in other places we we're helping the entire region so that has to be taken into consideration. I am being very aggressive with the state about our need to get more vaccines now," Breed said.
RELATED: Coronavirus Timeline: Tracking major moments of COVID-19 pandemic in San Francisco Bay Area
Besides City College, two other mass vaccination sites are set to open by Feb. 1 at Moscone Center and at the San Francisco Wholesale Produce Market.
They will be run in partnership with private providers like Kaiser Permanente, Dignity Health and Sutter Health.
Ramping up infrastructure is one thing, but the larger challenge right now is in securing vaccine supply.
There are some 200,000 people over 65 in San Francisco, the age demographic that represents 83% of the city's COVID deaths to date.
For more information on San Francisco's COVID vaccine plan, click here.
VIDEO: Coronavirus: San Francisco aims to vaccinate all residents by end of June, city leaders say
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