LOS ANGELES (AP) — A substantial number of California counties could see fewer restrictions on business operations starting next week as coronavirus infections, hospitalizations, and deaths continue to fall, Gov. Gavin Newsom said Tuesday. 

"The good news: Parts of the state are already beginning to open back up," Newsom said.

He spoke at the site of a new federally supported mass vaccination site in Los Angeles, which opened Tuesday along with a similar site in Oakland. The two sites are expected to get about 6,000 doses of vaccine a day, and are intended to vaccinate people in communities hit hard by the pandemic. 

The openings of the mass vaccination sites, heralded by a number of state and federal officials, came as California's virus numbers continue to improve even as demand for vaccine far exceeds capacity. 

About 3.5% of people being tested for coronavirus are getting back positive results, Newsom said, a rate that's dropped precipitously in recent weeks. The numbers of people in hospitals and intensive care units and case rates are declining — all factors in determining when counties can begin further reopening.

By next week, a "substantial" number of counties are likely to enter the "red" tier, which allows indoor dining at 25% capacity, and the opening of other indoor spaces such as movie theaters, museums and gyms with limits. 

California got about 1.08 million vaccine doses from the federal government this week, the governor said. The state expects 1.28 million doses next week and 1.31 million doses after that. The slow increase in the number of doses continues to frustrate local and state officials. 

Under a new vaccine distribution contract with insurer Blue Shield, the state set a goal of being able to administer 3 million doses a week, according to contract details released Monday.

But in recent days, mass vaccination sites like Dodger Stadium in Los Angeles and the Moscone convention center in San Francisco were temporarily closed due to lack of supply. Newsom said the state's goal is to build enough capacity so the state can quickly vaccinate people when more doses arrive. 

"We're building the infrastructure where the only constraint is supply," Newsom said. "But when the supply is ample, then we're able to move aggressively and quickly."

The mass vaccine sites opened in conjunction with the federal government on Tuesday will not draw from the same state supply, Newsom said.

The sites opened on the east side of the nation's second-largest city at California State University, Los Angeles, and on the east side of the San Francisco Bay Area at Oakland Coliseum. At Cal State LA, groups of cars pulled up to tents manned by military personnel. People were able arrive on foot or public transportation. 

The Federal Emergency Management Agency is hoping to open similar sites in Texas and New York, said Bob Fenton, FEMA regional administrator in California. When opening the sites, the government is focusing on areas where minorities make up more than 40% of the population, poverty rates, and lack of housing or vehicle access. The sites will also run mobile clinics that can go out to people who lack transportation.

"We're looking at high population areas among the states, but also ensuring that data drives us to the most socially vulnerable," Fenton said.