BOSTON — Eleven medical marijuana dispensaries were cleared by state public health officials on Friday to move forward, but nine others that had initially been given the green light were rejected after a further state review.

A company led by former U.S. Rep. William Delahunt, Medical Marijuana of Massachusetts Inc., and Good Chemistry of Massachusetts Inc., which had received provisional approval for dispensaries in Boston and Worcester, were among the firms turned aside.

A law approved by state voters in 2012 allows for up to 35 outlets to sell marijuana to patients suffering from conditions including cancer, HIV, multiple sclerosis and Parkinson’s disease. But implementation of the law has sputtered, and no dispensaries have yet been licensed.

Of 181 original applications, the Department of Public Health gave initial clearance to 20 proposed dispensaries in January. Reports later surfaced of potentially false or misleading information in some of the approved applications.

Karen Van Unen, head of the state’s medical marijuana program, said the 11 remaining facilities can make preparations to open, subject to final inspections. They would be in Dennis, Salem, Haverhill, Northampton, Ayer, Newton, Lowell, Quincy, Brookline, Brockton and Milford.

“We firmly believe that the applicants moving forward today are the ones that will be able to provide the highest quality services to our patients in the Commonwealth,” Van Unen said.

The earliest any are likely to open is November.

Medical Marijuana of Massachusetts had proposed dispensaries in Plymouth, Mashpee and Taunton.

Van Unen, in a letter to the company, questioned a business arrangement calling for the nonprofit firm to divert 25 percent of its gross revenue to a related, for-profit company controlled by several of the same executives as the nonprofit. The agreement violated state rules requiring dispensaries to operate solely on a not-for-profit basis, Van Unen wrote.

Good Chemistry was accused of misrepresenting statements of local support, including its claim to have met with the entire Boston legislative delegation, and that its meetings with Worcester officials included the chief of police and county sheriff.

Also rejected was a second dispensary in Boston – leaving the city without a single facility.