Enrollment in the new Bay State health insurance program for moderate-income residents reached 79,000 June 1, up 15% from the total recorded a month earlier, but consumers are just starting to use a newer program aimed at higher income residents, officials say.

A 2006 Massachusetts health insurance expansion law will require most individuals over the age of 18 to have health insurance that meets minimum coverage requirements starting July 1.

Experts believe that 160,000 uninsured, relatively high-income state residents should be buying health coverage through Massachusetts’ unsubsidized Commonwealth Choice program, which is supposed to negotiate for low rates and good benefit packages for individuals earning more than 300% of the federal poverty level, but the Commonwealth Health Insurance Connector Authority, the agency in charge of health insurance expansion efforts, is processing only about 100 Commonwealth Choice applications per week, officials say.

“People are slow in signing up,” says Lynn Wickwire, a representative for Health Care for All, Boston, a consumer group. “I doubt they’re going to get everyone signed up by July 1.”

Jennifer Chow, outreach and enrollment manager at Health Care for All, says agencies and nonprofit groups are continuing to ramp up enrollment efforts.

“Sign-up efforts will continue full force after July 1,” Chow says.

The state is using the Commonwealth Care program, which relies partly on Medicaid funding, to provide free coverage for residents earning less than 100% of the federal poverty level and subsidized coverage for residents earnings 100% to 300% of the federal poverty level. The program began opening to residents earning 100% to 300% of the federal poverty level in October 2006.

The Health Connector set up the Commonwealth Choice program for higher-income residents earlier this year. That program began accepting applications May 1 and is selling coverage that is scheduled to take effect July 1.

Despite low Commonwealth Choice enrollment figures, officials at the Health Connector Authority say they are seeing growing consumer awareness of the new health insurance requirements.

The 15% jump in enrollment in May “is a sign of success for health care reform,” Leslie Kirwan, chairman of the Health Connector Board, says in a statement. “The message that there are new opportunities to get high-quality, affordable health insurance is clearly getting out.”

Health Connector officials note that the agency’s Web site, at http://www.www.mahealthconnector.org, is getting twice as many page views per day as it was just a few months ago.

The Massachusetts Association of Health Plans, Boston, is pleased with the enrollment results, MAHP President Marylou Buyse says.

“The amount of progress is just incredible,” Buyse says “We’re very opportunistic about future enrollment.”