Enrollment in HealthCare.gov and state insurance marketplaces created under the Affordable Care Act opened smoothly and on time Sunday, although accompanied by further turbulence within a group of innovative health plans that the law pioneered.

“We are starting again. The marketplace is open for business,” Health and Human Services Secretary Sylvia Mathews Burwell announced, surrounded by balloons, jazz and steel-drum music, and banks of enrollment helpers in the lobby of the Martin Luther King Jr. Library in downtown Washington.

The kickoff fair in the District was among many community events planned nationwide in coming days to draw attention to the three-month window to sign up for coverage under a law that remains politically divisive five years after its passage.

Around the country, the first day was relatively quiet. HealthCare.gov, the online enrollment system on which 38 states are relying this year, opened at about 7 a.m. Eastern time as scheduled. During its first six hours, about 40,000 applications were submitted through HealthCare.gov., according to federal officials.

Separate exchanges established by a dozen states and the District also opened without incident.

Less overt drama surrounds this third year’s enrollment season, compared with the inaugural season, when HealthCare.gov and some state-run exchanges suffered massive computer defects, as well as last fall, when a pending Supreme Court case threatened to block federal subsidies that help consumers in more than three dozen states buy ACA coverage.

Still, big questions linger: Of the estimated 10.5 million uninsured people who are eligible to get coverage on the exchanges, how many can be persuaded to buy health plans? And how many of nearly 10 million existing customers will renew coverage — and at what price?

This fall, the most significant stumble has involved the nonprofit, consumer-focused health plans, known as co-ops, that the ACA created as competition for traditional insurers. Two more pieces of co-op trouble surfaced within the 48 hours before open enrollment began.

In Arizona, insurance regulators ordered that state’s co-op, Meritus, to close at the end of the year and removed it from the insurance exchange there. It became the 11th co-op in a year to decide to go out of business or be forced out by federal or state regulators.

And in New York, state insurance regulators and federal health officials on Friday abruptly moved up the closing date of the nation’s largest co-op, saying that its financial condition was “substantially worse” than they’d realized. Health Republic Insurance of New York now will fold on Nov. 30 — a switch that means its 210,000 members have just two weeks to pick a different plan for coverage in December.

In their promotional themes this year, Obama administration officials are asserting that consumers can find affordable health plans on the exchanges if they comparison-shop. That emphasis responds to surveys showing that cost concerns and confusion about subsidies are prime reasons that people have remained uninsured.

In their marketing materials this year and a spate of data analyses in the lead-up to Sunday, federal officials have played down an unpopular aspect of the ACA — its requirement that most Americans carry health insurance. People flouting that mandate are subject to a fine. For 2016, the penalty is $695 per person or 2.5 percent of a household’s income, whichever is greater.

National television advertising to promote enrollment will begin Monday with a smaller federal investment than in the past — $35 million, compared with $52 million for the first sign-up period two years ago.

In northern New Jersey, Wendy Sykes, executive director of the Oranges Navigator Project, said it will be “drilling down” this year to try to ferret out people who have not gotten coverage, including by working with college groups and religious organizations.

In the Rio Grande Valley of Texas, Cliff Clark, director of navigator programs at MHP Salud, said a few of the 16 people with appointments for enrollment help on Sunday were first-timers.

In the District, 16 enrollment assisters waited at long tables in the library during Burwell’s visit — many without a consumer across from them. By late afternoon, nearly five dozen residents had come through, according to a spokesman for the city’s insurance exchange, which sponsored the event.

Susan Levine contributed to this report.