Gov. Charlie Baker said Monday he would decide later in the week about whether to extend the statewide stay-at-home order. And in his daily press briefing, the governor was vague about whether the state would help rescue the financially struggling Steamship Authority.

The stay-at-home order, which closed all non-essential businesses, is set to expire May 4.

But with case numbers still high, the order is widely expected to be extended. “We believe it’s important for us to create some clarity around this . . . and you’ll hear from us later this week on that,” the governor said. “The trend data remains reasonably high.”

All six Island towns instituted their own, stricter stay-at-home orders that included bans on construction and landscaping in late March. The first phase of guidelines to relax those orders came into effect on Monday, allowing one and two-man crews to get back to work.

During the briefing Governor Baker also responded to a question about whether the state had plans to help the SSA. Ten days ago boat line general manager Robert Davis wrote a letter to the governor urgently seeking a bailout to help stem steep financial losses during the pandemic.

The SSA is a state-chartered ferry line that operates without subsidy. In the event of a deficit, the boat line’s enabling legislation provides for the state treasurer to provide funding that would later be repaid by taxpayers in the port communities.

The boat line has not had a deficit since 1962.

But on Monday Governor Baker said the state had limited jurisdiction over the SSA.

“The Steamship Authority is basically not an entity that we have jurisdiction over, for all intents and purposes,” the governor said. “And I believe most of their rule-making and regulatory oversight is federal. And I do know that this is a conversation that is going on currently with a number of similar entities with the federal government to determine whether or not there is a role for the feds to play there. The states, as a general rule, do not have jurisdiction, funding, anything to do with organizations like that, but the feds do.”

Since Mr. Davis wrote his letter, the boat line learned that it is already in line to receive $12 million in federal money, a combination of coronavirus relief and transportation grant funding. Over the weekend, Cong. Bill Keating announced that the funding would be expedited and arrive within the next two weeks. The money is expected to cover projected operating losses through July.

In a statement issued Monday afternoon, the boat line appeared to correct Governor Baker’s remarks while at the same time thanking him.

“As a public instrumentality of the commonwealth, the Steamship Authority falls under the jurisdiction of both state and federal authorities on a variety of matters,” the statement said. It continued:

“We have been working closely with the commonwealth, including calls today with officials from the executive office for administration and finance and the Massachusetts Department of Transportation. We have also been engaged with our federal congressional delegation and are grateful for their willingness to explore various financial relief options and potential opportunities. We are also thankful to Governor Baker, and all of those in his administration, for their attention to our unique issue, and look forward to more productive discussions to come as the full impact of the ongoing Covid-19 pandemic unfolds.”

Meanwhile, confirmed cases of Covid-19 on the Vineyard continued to hold steady at 16 for the third day in a row Monday, after no new cases were reported over the weekend.

Hospital officials also confirmed Monday that an early Saturday morning Coast Guard medical helicopter evacuation from the hospital was not pandemic related.

Hospital spokesman Katrina Delgadillo said a patient who had been hospitalized with Covid-19 was discharged in stable condition over the weekend, clarifying that the helicopter evacuation was for a different patient.

“The Coast Guard transfer was not Covid related,” Ms. Delgadillo wrote in an email to the Gazette.

Daily testing updates from the hospital include the number of patients currently hospitalized with the virus, but do not include information about patient discharges or medical transfers off-Island.

The hospital’s current policy is to transfer critical coronavirus patients to Boston whenever possible in an effort to protect its limited bed capacity. The hospital has three ICU beds and two ventilators.

The previous three Covid-19 hospitalizations on the Island resulted in medical transfers to Boston. Two were performed by Boston Medflight helicopters; the third was a maternity patient who was transferred to Boston via ground transport.

On Monday, the daily update from the hospital said that as of 10:30 a.m., it had conducted 365 tests, with 348 negatives, 16 positives and one pending.

Statewide, case numbers continued to trend high Monday, with 1,524 new cases and 104 new deaths, pushing the death toll past the 3,000 mark.