Many HealthCare.gov customers will face higher costs next year, the Obama administration acknowledged Thursday in a report that shows average premiums rising modestly.

However, officials said millions of consumers who are currently enrolled can mitigate the financial consequences if they are willing to shop around for another plan in a marketplace that’s becoming more competitive.

Premiums for the most popular type of plan will go up an average of 5 percent in the 35 states where the federal government is running the health insurance exchanges, said a report from the Health and Human Services Department.