Amid growing upheaval around governance at the Martha’s Vineyard Airport, members of the airport commission have declared they will serve out the remainder of their terms, despite a call from the Dukes County Commission to consider stepping down.

In a letter sent to the county commission this week, airport commission chairman Constance R. Teixeira wrote that commission members would “continue to discharge their responsibility until the completion of their statutory terms.”

Her letter came in response to a letter sent two weeks ago from county commission chairman Leonard Jason Jr. which asked the airport board to seriously evaluate its performance.

“The county commissioners believe the time has come for the airport commissioners to re-examine their behavior, their actions and their conduct in their meetings,” Mr. Jason wrote in the June 19 letter. “A public body that is in charge of the greatest asset of the county has an obligation to conduct their business publicly, politely and respectfully not only to the public but also to its members.”

When voting to send the letter, county commissioners expressed displeasure and concern over the way airport meetings had been conducted.

“They are all good people but put them together in one group and they just become dysfunctional,” Mr. Jason said at the time.

A reply was requested by July 1.

The county commission appoints the airport commission.

In their response, dated June 27 and signed by Ms. Teixeira, airport commissioners defended their behavior.

“The airport commissioners have . . . at all times conducted [themselves] in conformance with the requirements of open meeting law and consistent with long-standing airport commission best practices,” the letter says in part.

Ms. Teixeira wrote that the county had made the request “because you do not agree with recent decisions made by the airport commission.”

The airport commission recently filed a lawsuit against the county commission asking a judge to declare its legal autonomy in managing and administering airport affairs. The airport has also been the subject of a tangled workplace dispute involving a former employee and airport manager Sean Flynn. Last month Mr. Flynn was granted a paid medical leave of absence; assistant manager Deborah Potter has been named acting manager in the interim.

Earlier this year, the county commissioners ousted two of the incumbent airport commissioners in favor of new appointees. At the time, Mr. Jason cited the poor management of a personnel hearing held in public and televised on Martha’s Vineyard Community Television.

At an airport commission meeting last Friday morning, five commissioners voted to send the letter of reply to the county commission, while one commissioner, Christine Todd, opposed it.

Ms. Todd, who is also a county commissioner and a new appointee to the airport board, suggested commissioners should send individual letters in response. Ms. Todd said she had already sent her own response.

“It’s my belief that the commissioners are individually appointed and I just believe that the commissioners should individually reply, that is my opinion,” she said.

In her letter, she said she intended to continue as an airport commissioner.

“I fully intend to continue my pursuit of honesty, integrity, respect and transparency in this governing board of the Martha’s Vineyard Airport,” Ms. Todd wrote. “I feel my efforts and actions have begun to at least reveal the true character of the commission as it has existed.”

Commissioner Richard Michelson, also a new appointee, abstained on the motion. He indicated that he too would send his own letter. Reached Monday by telephone, he said he had not sent his letter yet and did not intend to resign.

“I have been there a short period of time and am trying to make some change,” Mr. Michelson said.