“We’re very pleased with our numbers,” Mr. Lee said during a news conference in Sacramento. “The word of a positive experience is quickly spreading.”

In all, 26,794 people enrolled in private plans through the federal exchange between Oct. 1 and Nov. 2, according to the Obama administration. In Texas, which has a higher percentage of uninsured residents than any other state, only 2,991 people enrolled.

California was one of the first states to start building an exchange and has been aggressive in publicizing it to potential customers. Still, Covered California, as the exchange is known, is far from its goal of signing up at least 500,000 people who qualify for federal subsidies to buy private coverage by March 31, when the six-month open enrollment period ends.

Of about 31,000 people who signed up for private plans in October, only about 4,850, or 16 percent, qualified for subsidies to help with premium costs. None of the enrollees have necessarily paid their first month’s premium, which is not due until late December. They could still change their minds and decide not to enroll after all. Coverage is to begin on Jan. 1.

California did not release demographic details about the enrollees, like where they live and how old they are. Some demographic data will be announced at a meeting of the exchange board next week. But Mr. Lee acknowledged that so far, a disproportionate number of enrollees are “older folks with health conditions.”