MENLO PARK — Nearly 70 percent of California’s previously uninsured adults have gained health insurance coverage under the Affordable Care Act — and most of them say their health care needs are being met, according to the latest survey of the Kaiser Family Foundation.

But the survey released Thursday by the Menlo Park-based group also found that plenty of challenges for the newly insured remain when it comes to paying for and accessing care. That applies both to those enrolled in plans through Covered California, the state’s health insurance exchange established under the Affordable Care Act, and Medi-Cal, the state’s program for the low-income and disabled that was greatly expanded under the health care law.

The survey results didn’t surprise some consumer health advocates.

“We have a long way to go towards affordability when half of the newly insured say they have a hard time affording health care, even as subsidies have been successful in expanding access and getting more low-income Californians insured,” said Carmen Balber, executive director of the Santa Monica-based Consumer Watchdog.

But the latest data was welcomed by many health care experts.

“For me, it was really the size of the gains in people’s sense of financial security and in their health care,” said Mollyann Brodie, director of public opinion and survey research at the foundation.

“I had hoped and thought that those numbers would go up, but I did not expect them to improve in those gaps as much as they did,” Brodie said. “It appears that getting health insurance really helps people to feel more financially secure and health secure.”

The foundation’s survey is the third of a series it began in 2013 that aims to track how the health care law, commonly called Obamacare, has affected the lives of the previously uninsured.

Since its debut in the fall of 2013, Covered California has enrolled 1.3 million Californians, while Medi-Cal has enrolled almost 4 million since January 2014.

Both the exchange and Medi-Cal have had problems. In the Covered California plans, many of the complaints have focused on the narrow networks of doctors and hospitals. And access to Medi-Cal doctors — already a chronic problem in a state that offers one of the lowest Medicaid reimbursements in the nation — only worsened with the expanded number of Medi-Cal enrollees.

But the survey found 83 percent of Medi-Cal enrollees and 63 percent of Covered California enrollees are mostly satisfied with their plans.

Other survey highlights:

Of the Californians who didn’t have insurance in 2013, 86 percent said it was difficult to afford health care. But in the latest survey, only 49 percent of the newly insured who were surveyed said it’s difficult to pay for health care.

The recently insured are about half as likely to say they have had problems paying medical bills in the past year (23 percent now compared with 45 percent in 2013).

When asked how well their health needs are being met, 86 percent of the recently insured now say they are being somewhat or very well met — up from 51 percent of the uninsured group in 2013. But 28 percent say that in the past 12 months they have had to wait longer than they thought was reasonable for a medical appointment.