BOSTON — Massachusetts residents suffering from multiple sclerosis, Lou Gehrig’s disease and other debilitating illnesses rallied at the Statehouse Thursday to call on Gov. Deval Patrick to speed up the process for opening medical marijuana dispensaries so they can safely purchase the drug.

Matthew Allen, executive director of the Massachusetts Patient Advocacy Alliance, said patients fear the dispensaries will not be ready to open by the summer as initially projected, because of delays in the licensing process.

“We’ve lost sight of what this is really about,” Allen said. “The process has become politicized. This is about compassion for people with serious illnesses who still do not have access to their medicine.”

The state Department of Public Health, which is charged with vetting dispensary applicants, said the approval process is ongoing but offered no timeline for when it might be completed. The department awarded 20 temporary licenses at the end of January, but is still verifying the applications.

Spokesman David Kibbe said the department is trying to strike the appropriate balance between “patient access and public safety.”

Massachusetts’ medical marijuana law took effect in January 2013, allowing physicians to recommend marijuana to patients for the treatment of a range of ailments, including cancer, glaucoma, AIDS, Hepatitis C and Parkinson’s disease.

The law also established a state registry of medical marijuana patients and allowed for creation of up to 35 state-licensed dispensaries.

Advocates also called on the state to increase the number of patients an individual may sell medical marijuana to. Under state regulations, a “caregiver” can only provide marijuana for one patient at a time. The limit is five patients in neighboring Rhode Island and Maine.

“Right now there’s no constant or consistent supply,” said Nichole Snow Dawson, who said her husband suffers from neurofibromatosis. “My husband is forced to go to the black market and sometimes do without medicine at all.”

Massachusetts’ medical marijuana law took effect in January 2013, allowing physicians to recommend marijuana to patients for the treatment of a range of ailments, including cancer, glaucoma, AIDS, Hepatitis C and Parkinson’s disease.

The law also established a state registry of medical marijuana patients and allowed for creation of up to 35 state-licensed dispensaries.

Thursday’s rally came as state lawmakers held a hearing on a proposal to legalize and tax marijuana outright.

Introduced by state Rep. Ellen Story, D-Amherst, the legislation would allow adults aged 21 and older to possess and grow marijuana. It would also establish a “Cannabis Control Authority” to tax and regulate the drug.

Matt Simon, of the D.C.-based Marijuana Policy Project, said it’s time for Massachusetts to join Colorado and Washington in creating a regulated cannabis market where drug profits can go to taxpaying businesses rather than underground criminal organizations.

Simon noted that Massachusetts has already made two significant changes to its marijuana laws: decriminalization of possession of an ounce or less of the drug and creation of a medical marijuana program.

Story’s bill was heard by the Joint Committee on the Judiciary, which was not expected to vote on the measure Thursday.