Covered California officials released the figure in the first of what they say will be a series of weekly updates on the number of applications and calls received by the insurance exchange.
An additional 27,300 California households have started to fill out an application. Applications can cover more than one person, such as a spouse or child.
Covered California executive director Peter Lee described the initial interest in the new health coverage as "phenomenal."
"These are big numbers, and they're proof of the pent-up demand for coverage that is here in California and is also across the nation," he told reporters during a news conference.
State exchange officials had anticipated "very low" enrollment during the first week, but did not have an internal projection for how many applications they might initially receive, Lee said.
It's difficult to fit the number released Tuesday into a broader context because the exchange, set up under the federal Affordable Care Act, is new and because consumers have until March 31 to sign up for coverage in 2014. By comparison, 15,000 applications were completed by Monday in Kentucky, a state with a population that is less than 12 percent of California's. Almost half of those applicants went on to buy an insurance plan, according to the Kentucky governor's office.
The 16,311 applications completed in California through Saturday were processed to determine whether the consumer is eligible for federal subsidies to decrease their monthly costs or to enroll in the state's low-income insurance program known as Medi-Cal.
Applicants are not officially enrolled until they have selected a health plan and paid their portion of the premium. Covered California officials said they will not release the number of applicants who have taken those steps until monthly enrollment reports begin in November.
Tuesday's update came as the federally run exchanges remain hampered by technical problems that are slowing the enrollment process.
Call centers supporting California's insurance exchange handled more than 59,000 telephone inquiries in the days after the Oct. 1 opening of the marketplaces, Lee said. Wait times that reached 40 minutes were reduced to less than four by Friday, he said, adding that officials are aiming for wait times of less than 30 seconds.
The exchange website received more than 987,000 unique visitors last week. It faced some technical difficulties on its first day, which required the enrollment section to be taken offline twice for fixes.
Officials say they are continuing to add online features, including a search tool so Californians can check whether services from a particular doctor or hospital are covered by a health plan.