Massachusetts is set to receive thousands more doses of COVID-19 vaccines each day, providing a notable boost to the constrained federal supply that Governor Charlie Baker has said is the greatest limitation on the state’s efforts to inoculate all eligible residents.

Federal and state officials announced Friday that the Hynes Convention Center in Boston will soon begin receiving 6,000 additional federal doses daily, adding to the 1,000 daily doses the state has been supplying to the site.

The news comes as coronavirus cases in Massachusetts are beginning to tick up again, and as the rate of vaccinations wavered up and down over the past two weeks. National data show Massachusetts is among the top states in percentage of residents who have received a first dose. Nationally and in Massachusetts, white individuals have been vaccinated at higher rates than people of color, though Massachusetts has vaccinated a higher percentage of its Black population than most states.

The program will be open to the public, with additional services for Suffolk County communities that have been most impacted by the virus, starting March 31. State officials said the site was selected based in part on the CDC’s Social Vulnerability Index, which considers variables including socioeconomic status and housing type. Paul Ford, who oversees FEMA’s operations in New England, said the center aims to increase the vaccination rate efficiently and equitably, “with an explicit focus on making sure communities with a high risk of COVID-19 exposure and infection are not left behind.”

“Massachusetts is a national leader for vaccines and this additional support from the federal government will help to increase access and availability to some of our most disproportionately impacted communities,” Baker said.

Baker said Thursday that in addition to its normal weekly allocation — which was 330,000 for this week — the state expects to receive an additional one-time allocation of 40,800 Johnson & Johnson doses and 20,000 Pfizer first doses next week.

Baker touted the good news but cautioned that the federal supply to Massachusetts still does not match demand for the vaccine among eligible residents.

The Hynes Convention Center, not far from Fenway Park and the Prudential Center, is near many of Boston’s wealthier enclaves, like the Back Bay neighborhood. But state officials noted it is accessible via several MBTA lines.

Some doses will be designated for mobile units in areas including Chelsea and Revere. The site will have interpreters available for individuals who speak Spanish, Mandarin, and Haitian/Creole, as well as access to a telephonic translation service with access to 240 languages.

Senator Elizabeth Warren praised the effort, saying “this program will provide the necessary resources and support to complement the ongoing efforts by the Commonwealth to prioritize disproportionately impacted communities that have greatly suffered from the COVID-19 pandemic.”

The Hynes Convention Center is among a several mass vaccination sites opened by the state. Vaccines are also being administered at dozens of other sites including pharmacies, hospitals, and other venues.

“CIC Health designed the vaccination site to scale, so we know the Hynes Convention Center has the ability to handle this increase in vaccinations,” CIC Health, which operates the site, said in a statement Friday. “The CIC Health team stands ready to manage the administration of the vaccines in collaboration with federal and State personnel and to ensure a great experience for our guests from start to finish.”