Residents 65 and over, and those with two underlying health conditions, will become eligible for COVID-19 vaccines starting today

State officials said it was time to allow the new groups into the vaccination pool because 850,000 of the 1.1 million who are already eligible — including more than half of those over 75 — have received the first dose of the two-dose vaccines. The state’s goal is to fully immunize 4.1 million adults.

But the move raised public expectations at a time when state officials acknowledged it still may take weeks for people to schedule appointments. It also marked the latest adjustment by the Baker administration as it responds to public criticism and seeks to manage the complex rollout.

“It’s a positive step,” said Dr. Howard Koh, professor at the Harvard T. H. Chan School of Public Health. “But with every step, the question is: Can supply meet demand in a way that’s viewed as timely, convenient, and fair?”

Advocates for the state’s baby boomers were delighted at the announcement. People age 65 to 74 have been waiting since Feb. 1 to learn when they could get immunized.

“It’s been a long time coming,” said Mike Festa, director of AARP Massachusetts, which has lobbied for extending vaccine access to the over-65 group. “These are the ones most vulnerable to COVID and they’re anxious. [Thursday] morning at 8 a.m. is going to be a pretty crazy time.”

But even as many more residents looked forward to being immunized against the coronavirus, Governor Charlie Baker warned them to be patient.

“Unless we see a massive increase in shipments from the feds, it will take us at least a month for [all] people in these new groups to be able to book their first vaccine appointment,” Baker said at the State House.

Baker said residents flocked to the state’s website Wednesday morning after word of the change first got out, a sign of pent-up demand, even though sign-ups for the new groups don’t actually start until Thursday.

“I think we had 250,000 visits to the state’s website,” the governor said.

The state will also continue its controversial “companion” program, which allows younger people to get shots if they bring people 75 and older to mass vaccination sites, officials said. The companion program does not apply to those who accompany the newly eligible over-65 group, however.

Despite a limited supply of the vaccine from the federal government, Baker said Massachusetts is accelerating its vaccination drive — he called it a “top 10 state” now in injecting first doses per capita — by pivoting to mass vaccination sites and regional collaboratives, from Cape Cod to the Berkshires.

“The big message we got from the public was vaccinate, vaccinate,” Baker said. “And there’s no question the fastest way to do this is with high-volume sites.”

Secretary of Health and Human Services Marylou Sudders, in an earlier briefing, said Baker administration officials have received word from the federal government that supplies are increasing. Massachusetts will begin getting 139,000 first doses starting this week, a more than 25 percent boost, with the extra doses coming from vaccine maker Pfizer-BioNTech.

But she, too, cautioned that the bump almost certainly won’t be sufficient to vaccinate all those who want shots right away. The state is still “not where we need to [be to] vaccinate everyone in Massachusetts,” she said.

Given the hazy outlook for future shipments, Nada Sanders, professor of supply chain management at Northeastern University, said the state should have opted for “a more surgical approach” by extending eligibility to smaller groups.

“You’re talking about a huge surge in demand when you’re dealing with a limited supply,” Sanders said. “At the end of the day, it’s all about matching supply and demand.”

But state officials chose to offer the vaccine to broad groups, including people suffering moderate to severe asthma that puts residents at higher risk for COVID-19, a respiratory illness.

Other qualifying medical conditions include cancer; chronic kidney disease; chronic obstructive pulmonary disease; Down syndrome; heart conditions, such as heart failure and coronary artery disease; being immunocompromised; pregnancy; sickle cell disease; obesity; smoking; and, type 2 diabetes.

Baker said that making people with asthma eligible is vitally important to reaching hard-hit communities.

“There’s tons of studies that have been done that demonstrate that at-risk communities and communities of color have historically had higher rates of asthma,” he said.

Not everyone was pleased with Wednesday’s eligibility expansion. State officials gave no date for when those who are now next in line — essential employees ranging from teachers to grocery clerks — will be able to get their shots.

And while disability rights activists commended the administration’s decision to add asthma to the list of eligible conditions, many were disappointed other chronic illnesses and conditions, such as cystic fibrosis, HIV, and spinal cord injuries, are still being excluded.

“The clock is ticking,” said Colin Killick, executive director of the Disability Policy Consortium in Malden. “Every day that those conditions aren’t approved and moved to the front of the line is another day when those people aren’t getting vaccinated and are at risk.”

Nicole Lomerson of Northborough, has cerebral palsy and uses a wheelchair. The degree of her disability, she said, would qualify her to live in a nursing home. But she still does not qualify for access to the vaccines in Massachusetts.

“The only people who fight for people with disabilities to get access to the things we need to stay alive are people with disabilities themselves,” Lomerson said.

To speed its vaccination program, Sudders said, the state is sending more doses to four mass vaccination sites — Fenway Park, Gillette Stadium, the DoubleTree hotel in Danvers, and Eastfield Mall in Springfield — and 13 sites run by regional collaboratives that will take any state resident. Two more mass injection sites will be opening soon in Natick and Dartmouth.

Massachusetts officials plan to post 70,000 new appointments for shots at the mass vaccination sites on its website mass.gov/covid-19-vaccine on Thursday. Other slots can be booked at some smaller sites, such as CVS and Walgreens pharmacies and community health clinics. Vaccine appointments can also be booked through the state’s new call-in center by dialing 211.

Ninety-five percent of Massachusetts residents live within a 45-minute drive of a mass vaccination site and a 35-minute drive of a large regional site, Sudders said.

At the same time, the state is suspending new first doses, starting March 1, to most local boards of health that run municipal clinics open only to residents of their communities.

Those local clinics will still get second doses for residents who’ve already gotten first shots. And state health officials will work with local governments to vaccinate thousands of frail or disabled homebound residents who are unable to travel to vaccination centers.

Local health directors said they were caught off-guard by the state’s announcement. They worry the new rules will shut out smaller communities near a mass vaccination site from receiving doses that would be used to vaccinate homebound residents. And they’re not sure if their local facilities will qualify to vaccinate others they had planned for, such as local teachers and school employees, when those groups become eligible.

“We have a lot of questions,” said Sigalle Reiss, president of the Massachusetts Health Officers Association and Norwood’s health director. Reiss said local health departments received state and federal money for more than a decade to plan and train for mass vaccinations.

“It’s just out the window now,” she said.

The cutoff won’t apply to 20 cities and towns with heavy coronavirus caseloads: Boston, Brockton, Chelsea, Everett, Fall River, Fitchburg, Framingham, Haverhill, Holyoke, Lawrence, Leominster, Lowell, Lynn, Malden, Methuen, New Bedford, Randolph, Revere, Springfield, and Worcester.

Those communities are covered by a new initiative aimed at making it easier for people to get immunized in high-risk cities and towns disproportionately hurt by the pandemic.

Sudders also said that while vaccine supplies were cut to Massachusetts hospital systems and their affiliated doctors last week, she expects hospitals will continue to be part of the state’s vaccination drive as supplies increase.

“This is a constrained supply as we add new eligibility groups,” Sudders added. “So we need people to be patient.”

Robert Weisman can be reached at robert.weisman@globe.com. Deanna Pan can be reached at deanna.pan@globe.com. Follow her @DDpan. Travis Andersen can be reached at travis.andersen@globe.com. Kay Lazar can be reached at kay.lazar@globe.com Follow her @GlobeKayLazar.