Maryland officials reported a modest uptick Friday in the number of people choosing to enroll in private plans through the state’s online health-insurance exchange and said a new round of data coming next week would show “a marked increase” in total enrollments.

As of Nov. 30, a total of 3,758 Marylanders had chosen to enroll in private plans through the Maryland Health Connection, an increase of 734 from the previous week, state officials said. The state, which launched the exchange on Oct. 1, has set a goal of enrolling 150,000 people by the end of March.

The weak start has been largely blamed on glitches with the state’s Web site — and become a source of fodder in the 2014 governor’s race.

Attorney General Douglas F. Gansler has repeatedly chided his Democratic primary rival, Lt. Gov. Anthony G. Brown, for the problems. Brown co-chairs a council responsible for overseeing health-care reform in Maryland.

Maryland has lagged behind other states that elected to run their own insurance exchanges as part of the new federal health-care law.

Brown said this week that he was among those responsible for the exchange’s problems and pledged to hold a media availability session next week to talk at greater length about the state’s progress.

Gov. Martin O’Malley (D) has set a mid-December target for fixing most of the glitches.

The numbers released Friday do not reflect activity during the past week. In its report, the state said activity on the Web site has been “robust” in recent days.

“We expect next week’s data to illustrate a marked increase in total enrollments,” the report said.