Construction bans enacted on Martha’s Vineyard and Nantucket will remain in place, following a conference call late Sunday with a wide-ranging group of officials from both Islands and three senior executives for Gov. Charlie Baker.

“The governor’s representatives stated that the local boards of health retain the power to ban construction if warranted by local considerations,” a statement posted on the Edgartown website said Monday morning.

“The orders of our local boards of health expire on April 7. During the next week, we intend to work with construction trades to develop a protocol for what happens after that date,” the statement also said.

The telephone conference call held late Sunday afternoon included selectmen, boards of heath, police chiefs and fire chiefs and the CEOs of the Martha’s Vineyard Hospital and the Nantucket Cottage Hospital. Cape and Islands Sen. Julian Cyr and Rep. Dylan Fernandes also participated.

Representing the governor on the call were chief legal counsel, chief of staff, and legislative liaison, according to the statement.

The standoff between the two Islands and Governor Baker over the construction ban during the coronavirus pandemic began last week when Robert Ross, the governor’s chief legal counsel, sent a letter notifying commonwealth cities and towns that they cannot adopt orders that are stricter than Governor Baker’s advisory for a stay-at-home order issued early last week. When the letter went out, construction bans were already under way in Island towns.

Responding quickly, a wide coalition of leaders on both Islands, including some builders and contractors, assembled to oppose the directive from Beacon Hill, firing off a blunt letter notifying Governor Baker that overturning the construction ban would put the health and safety of the two Islands at risk.

The Island hospitals, with 25 beds on the Vineyard and 14 on Nantucket, are preparing for a surge in Covid-19 cases, which is expected in the weeks ahead.

By Monday morning it appeared that the governor had recanted.

In an email to Mr. Cyr after the phone conference, Mr. Ross said Governor Baker’s essential services order depends on local enforcement, signaling that municipalities had the authority to ban construction if they felt it could not be conducted safely.

“Governor Baker’s [order], like most of the other orders he has signed during this crisis, depends on local enforcement,” Mr. Ross wrote. “While the order prescribed statewide designations of essential services to accomplish consistency and unity of purpose, both the order and my March 25 letter included requirements that ‘essential services’ be conducted safely. In the context of construction projects, that means that the municipality must be satisfied that a project can be conducted safely.”

In a followup email to Mr. Ross Monday morning, Senator Cyr pressed the chief legal counsel on the takeaway from the Sunday conference call.

“Representative Fernandes and I would like to further memorialize our conversation on March 29,” Senator Cyr wrote. “Per our conversation, towns on Martha’s Vineyard and Nantucket who cannot guarantee that construction projects are conducted safety are able to employ their authority under their board of health to halt these projects. As discussed, each of the seven island towns have well documented the public health concerns and exposure risks associated with construction projects. Is this correct?”

In a separate email that went out to Island town administrators Monday morning, Mr. Cyr elaborated further: “Regarding construction projects, the municipality must be satisfied that a project can be conducted safely. If the town cannot guarantee that construction projects are conducted safely, they are able to employ their authority under their board of health to halt these projects.”

West Tisbury town administrator Jennifer Rand, who participated in the Sunday conference call, said she believed everyone came away with the same understanding: that boards of health have the authority to enact a construction ban out of concern for public health and safety.

“We were all on the same call,” Ms. Rand said. “I don’t think any of us walked away with a different interpretation.”

Ms. Rand said town leaders told the governor’s office in the bluntest terms the dire nature of the Islands’ limited resources.

“What was expressed to the governor was our concern that our hospitals, Martha’s Vineyard and Nantucket collectively, absolutely positively can’t handle any extra. We can’t handle extra construction injuries. We can’t handle extra infections from people coming over on the boat every day to work. We don’t have the capacity. And we are unique in that we have people coming over every day on the boat to work.”

An earlier version mistakenly attributed a quote to chief legal counsel Robert Ross. The quote was from an email sent by Sen. Julian Cyr to Island town administrators. The story has been corrected.