SANTA CLARA COUNTY — Health officials in Santa Clara County say the “continuing insufficient” coronavirus vaccine supply they are receiving from the state may not improve significantly for “a few weeks,” forcing them to cancel thousands more first-dose appointments across the region.

“All we need to dramatically expand access to vaccinations is more vaccine, and we are ready and waiting for it,” said County Executive Jeff Smith in a statement Thursday.

County officials have continued to bristle at the state’s vaccine rollout, after loudly pushing back against plans to have insurance giant Blue Shield run the state’s vaccination program.

Millions more Californians became eligible for shots Monday, and the insufficient vaccine supply means many of them may not be able to schedule an appointment for weeks.

The county on Thursday said it again notified “several thousand” Kaiser patients their vaccine appointments scheduled at county vaccine sites between March 22 and March 28 will be canceled.

Those patients will be transferred back to Kaiser, which the state has assured will have enough doses for its members, according to the county statement. The county also had to cancel thousands of Kaiser patient appointments earlier this month.

“The lack of sufficient supply from the state has been frustrating for everyone, particularly those who are eligible for the vaccine, and want to be vaccinated, but have been unable to sign up,” said Marty Fenstersheib, the county’s head of testing and vaccine, in a statement.

The county expects vaccine supply to “increase significantly statewide in a few weeks,” bolstered by additional shipments of the one-dose Johnson & Johnson vaccine. The state pledged earlier this month that a reliable flow of vaccines will arrive in early April, but details about the likely distribution for those doses are thin.

“We want to see the significant capacity we have built in full use, and we look forward to opening up first-dose appointment capacity more broadly as soon as vaccine supply allows,” Smith said.

Despite the current shortage, the county said it is focusing on using its limited supply of first-dose shots to vaccinate the “most disproportionately affected communities” in the region, such as food service workers and farmworkers in South County.

The county said it vaccinated food and agricultural workers at Lusamerica Foods and Kawahara Nursery in Morgan Hill this week. On Friday, it will operate a clinic in partnership with Olam Spices and the United Farm Workers Foundation in Gilroy, which will be open to workers from other farms.

“These vaccination events in South County at food production facilities and farms are critical to reaching our front-line workers most at risk,” said Deputy County Executive Rocio Luna.

A special four-month investigation by this news organization found that Latinos in six Bay Area counties have case rates more than four times those of White residents, and large disparities in testing and vaccination are persisting.

“The county will continue to do everything we can to ensure equitable access to vaccination and to prioritize communities at greatest risk,” Luna said.

Limited first-dose vaccine shots are also being offered through community-based sites in East San Jose and at the Eastridge Mall in conjunction with Stanford Health Care, the county said. Preparations are also underway for drive-through vaccinations at Gilroy High School, where a walk-in site is already running.

Information about when and where you can get a vaccine in the county is available at sccFreeVax.org.