In a surprise announcement Wednesday, Gov. Charlie Baker opened Covid-19 vaccinations to all residents 65 and over and those with two or more underlying conditions starting Thursday — and local vaccination sites scrambled in response.

Signup for eligible residents on Island will begin Saturday morning, with the first appointments available for Monday, Martha’s Vineyard Hospital officials said in a follow up briefing later Wednesday. The signup process will occur online at the hospital’s website, and appointments will be available on a first-come, first served basis.

At the briefing, hospital officials urged patience.

“Due to extremely high demand for appointments and limited vaccine supply, it could take more than a month for all eligible individuals to secure an appointment,” said hospital head of operations Claire Seguin. “And this is all dependent on the supply from the federal government.”

Governor Baker’s announcement said 70,000 appointments had been made available at the mass vaccination sites across the commonwealth, and that starting Thursday, eligible residents could sign up through the state Department of Public Health website at https://www.mass.gov/covid-19-vaccine.

The state website crashed soon after it opened Thursday morning.

The closest mass vaccination sites to the Vineyard are located in New Bedford and at Gillette Stadium in Foxborough; there is no mass vaccination site on Cape Cod. The hospital is functioning as the Island’s general vaccination site.

During the briefing, hospital officials said signups would not open until Saturday because of supply. Unlike the scheduling process for Islanders 75 and older, eligible residents will not be contacted via email through Patient Gateway or by the hospital. Instead, anyone 65 or older, with two or more co-morbidities, or any resident of elderly or low income housing will be able to make an appointment through a scheduling tool that will go live on the hospital’s website Saturday morning.

Officials said they had not decided on a time.

The web tool will offer available appointments through the upcomming week, and will be expanded when more supply becomes available. The hospital hopes to vaccinate 1,800 people beginning next week, according to Ms. Seguin, which includes second dose vaccines for people in earlier phases. Officials said the signup is similar to the Steamship Authority process — except there is no wait list.

“Community members are encouraged to keep checking the hospital website as appointments will be added on a rolling basis,” Ms. Seguin said.

The hospital has vaccinated more than 2,500 Island residents so far, including hundreds of health care workers and first responders in phase one of the state rollout, and more than 1,000 residents over 75. But aspects of the process have been confusing, including a recent email from Patient Gateway saying hospitals had halted the vaccine rollout, which did not apply on-Island.

Officials felt the new system would be simpler, and expressed confidence that the website could handle the traffic. They also ackowledged the potential for pandemonium.

“Everybody’s fingers are crossed,” hospital CEO Denise Schepici said. “I think we have it covered.”

“This way is actually easier in our mind,” Ms. Seguin said. “People can directly schedule themselves at a time that’s convenient to them instead of waiting for outreach from Patient Gateway or the hospital.”

According to the governor’s announcement, underlying conditions that qualify as co-morbidities include asthma, cancer, chronic kidney disease, heart conditions, weakened immune systems from organ transplants, obesity, pregnancy, sickle-cell disease, smoking and type two diabetes. Anyone 16 or older with two or more conditions is eligible to sign up for the vaccine.

Along with those 65 and older, residents and staff of low income and affordable public and private senior housing are eligible to receive vaccine effective Thursday. Hospital officials confirmed that Vineyarders eligible included all staff and residents of Island Elderly Housing, Morgan Woods, Henrietta Brewer House, Mayberry and Havenside developments.

The state said the new phase of the vaccine rollout made more than one million state residents eligible for the vaccine, but added that the process could be slow because of federal supply issues. Signup at state mass vaccination sites is essentially the same as the hospital’s process, officials said.

Hospital officials said they hoped to vaccinate between 300 and 500 Islanders per day during this phase of the vaccine rollout. Ms. Seguin added that the vaccination process was not finished for Islanders 75 or older, either — estimating it was just shy of the approximately 2,000 on-Island.

“We’re pretty much close to being finished with the people that we know about,” Ms. Seguin said. “I think we’ve done the vast majority.”

But with eligibility expanded, officials did not know how many Islanders now qualified for the vaccine.

“This is a large group,” Ms. Schepici said. “I don’t know the exact number . . . not everybody is going to get an appointment on day one, so we just ask for everybody’s patience as we work through supply. The appointments are all going to depend on supply.”

Also Wednesday, state Sen. Julian Cyr joined 92 others in a scathing letter to the governor urgently requested a mass vaccination site on Cape Cod.

“In the most significant vaccination effort in Massachusetts history, Cape Codders are being left behind,” the letter said. “The situation on the ground is untenable and must change.”

The process for Island signup, provided by the hospital, follows:

• Go to the website mvhospital.org/patients_and_visitor/covid-19-updates

• Click the “COVID Vaccine Open Scheduling” link on the webpage.

• Confirm your eligibility by selecting “yes” after you attest that you belong to a current priority group.

• If you are eligible, select “Martha’s Vineyard Hospital” as a location.

• Schedule your appointment during an available time slot.

• Review information to ensure it is correct and then select SCHEDULE IT.

• The scheduling tool is expected to go live Saturday morning.