Frustration about the state's rocky COVID-19 vaccine rollout and its impact on older adults continued to escalate Thursday, even as Gov. Charlie Baker promised more appointments would become available and the launch of a new call center to help with scheduling.

Lawmakers lobbed new rounds of criticism at the administration for funneling residents 75 and older to the state's website to try to book vaccine slots, arguing that many do not have reliable internet access or the technologic literacy needed to navigate the site. Other older residents face difficulties in traveling outside their homes, particularly during a deadly pandemic.

Sen. Anne Gobi of Spencer called the rollout a "total nightmare." Eight representatives flagged "deep concerns" with the distribution plan in a Wednesday night letter. Sen. Harriette Chandler, who at 84 will qualify for the vaccine in the start of Phase 2 next week, tweeted that she thought of herself as equipped to navigate the digital landscape until "the state's vaccine website proved me wrong."

Just hours after he filed it, more than four dozen legislators had already cosponsored a Sen. Eric Lesser (D-Longmeadow) bill (SD 300) aimed at immediately forcing the Baker administration to launch a new phone-based system for securing appointments and an easier-to-use centralized web portal.

"I've heard and my colleagues have heard from their constituents in every corner of the state that the system is confusing, that it's inconsistent," Lesser said in an interview. "It's really just frankly a maze of links and various, sometimes-contradictory instructions that seniors have to navigate in order to book the appointment."

At a press conference to announce a new round of funding awards to struggling small businesses, Baker said his team is already working to stand up a call center to help book appointments for those who cannot or do not want to use the state's website. Baker said he "would have liked" to have the phone option ready already, but indicated it will launch next week.

"We've been staffing call centers since this pandemic began and we've been staffing them in a pretty big hurry, in many cases, on some fairly complicated topics," he said. "We're pretty good at it. We're late, but we're pretty good at it. I don't worry about whether or not the call center will be able to serve people appropriately. It will."

Lesser argued, though, that Baker's comments do not make it clear if the administration's call center will guarantee connection with a live human and several language options as the bill would require.

Mike Festa, state director of AARP Massachusetts, said his organization had been advocating for the administration to create a dedicated phone line, noting that many older adults prefer to speak directly to someone -- especially on a topic as important as securing a vaccine -- than to use a computer.

Vermont and New Hampshire already have live call centers established, Festa said, leaving the lack of a similar option in Massachusetts "really disappointing and surprising."

"If you only allow people to enroll on a website, you are missing whole swaths of seniors who have no access to the internet or, if they do, are really not comfortable enrolling or making their applications or appointments," Festa told the News Service. "Our message to the government has been, look, you've just got to meet people where they are."

Many smaller vaccination locations in Massachusetts such as pharmacies are adding more appointments every day, while the state-established mass vaccination sites will start posting a block of slots every Thursday for the week ahead.

The Baker administration said 10,000 appointments were posted in Springfield and Danvers on Wednesday and were filled within hours. On Thursday, Springfield and Danvers made another 15,000 appointments available, and Gillette Stadium and Fenway Park posted a total of 20,000 appointments. CVS Health will post 1,152 new appointments daily across eight sites, for a total of 8,000 per week, the administration said.

Baker acknowledged that the first day older adults could schedule appointments online was "a very frustrating day," and renewed his frequent caveat that there are "far more people who are eligible to get a vaccine than there are vaccines available."

Supply has been an issue since the state first started vaccinating the highest-priority residents last month.

President Joe Biden this week announced that his administration would boost distribution to states for at least the next three weeks and place larger orders with Moderna and Pfizer, part of an effort to vaccinate 100 million Americans in his first 100 days in office.

But even with an increased weekly shipment of 100,000 doses instead of the usual 80,000, Baker said the demand is far greater than the supply.

"There are currently somewhere around a million people, plus or minus, in Massachusetts who are eligible to get vaccinated," Baker said. "With 100,000 new doses a week, you can do the math and figure out that might mean it will take a little while for you to have the opportunity to get your first vaccination."

According to data compiled by the Centers for Disease Control, Massachusetts ranked 40th out of 59 states, territories and federal entities for COVID-19 vaccine doses administered per capita where that figure is counted as of Thursday, lagging every other New England state.

Baker said Thursday that his administration wanted to avoid "a place that a number of other states have ended up in, where people have made appointments, and they've been told, either when they showed up or the day of, that there was no vaccine available for them."

Lesser said most Massachusetts residents recognize the constraints created by low vaccine supply. He argued, though, that supply does not explain why the Bay State is behind its neighbor and peer states or some of the gaps in communication.

"People are willing to be patient," Lesser said. "They have been patient for month after month after month of this. But what people aren't going to tolerate is mass confusion and, frankly, a dismissive attitude about the problem, which is what has been signaled to us."

Almost all of the lawmakers who have backed Lesser's bill are Democrats, though cosponsors did include Republican Reps. Steven Xiarhos of Barnstable, Peter Durant of Spencer and Susan Gifford of Wareham as well as independent Rep. Susannah Whipps of Athol.

Baker promised to offer more information next week about the in-progress call center and other resources the administration will make available to help older adults. In the meantime, Baker urged residents to remain patient and persistent.

"If you don't see an opening at a site that's interesting to you or a place you'd like to go, you should just go back," Baker said. "Go back to that site each day. Eventually, an opportunity will become available, and you can take it."

For many other officials, the administration's timeline is too slow or too uneven.

Attorney General Maura Healey, a Democrat, slammed the Baker administration for not launching a phone-based option for booking appointments at the same time as the state website to which it directed adults 75 and older on Wednesday.

"First, it was unemployment. The Department of Unemployment had no live call center," Healey tweeted Thursday. "Then, it was workplace safety. After that, evictions. No system. We've tried to help those frustrated constituents all year. The vaccine call center should have happened yesterday."