Embattled Boston Fire Chief Steve E. Abraira, facing sharp criticism from his command staff over his management style and response to the Boston Marathon bombings, is threatening to sue his deputy chiefs if they continue launching what his lawyer claims are “defamatory” attacks.

In a letter sent to the deputies last week and obtained by the Globe, Abraira’s lawyer, Louis M. Ciavarra, referenced an earlier letter critical of Abraira that 13 deputy chiefs sent on April 26 to Mayor Thomas M. Menino.

The deputies wrote that the fire chief showed no leadership after the bombings and acts as a spectator at major fire scenes, instead of taking command as his predecessors did.

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In response, Ciavarra wrote that his firm is prepared to file a lawsuit “should any further such conduct occur” to put a stop to it and obtain damages.

“Your conduct is nothing more than a transparent effort to hide the inadequacies of your own performance and to interfere with my client’s efforts to improve the Boston Fire Department,” Ciavarra wrote to the deputies.

He said the “timing of your letter, and in particular, linking it to the tragedy of April 15th is reprehensible” and “was a misplaced and frankly outrageous attack intended to strengthen your ability to reject and obstruct Chief Abraira’s efforts to bring the BFD in line with modern fire fighting practices.”

Joseph G. Donnellan, a lawyer for the deputy chiefs, fired back on Thursday. He said his clients view Ciavarra’s letter as an attempt to keep them from testifying at a City Council hearing scheduled for June 18 to address the issues they raised.

“Each and every one of them saw it that way,” Donnellan said. “They saw it as a direct attempt to make sure these guys don’t go to that hearing and don’t speak their mind.”

Donnellan said the deputy chiefs will counter-sue if Abraira brings a civil action against them.

“Most assuredly, if the chief’s lawyer follows through on his threat to sue the deputy chiefs of the Boston Fire Department, we will react very strongly and very swiftly,” Donnellan said.

Abraira did not return a call seeking comment on Thursday.

He has previously said that he felt his command staff had the Marathon scene under control by the time he arrived, and that according to national standards, chiefs have the option to take command at scenes but are not required to.

Asked about the allegation of attempting to silence the deputies at the upcoming hearing, Ciavarra, the lawyer for Abraira, said on Thursday that he was not aware it had been scheduled.

He also addressed an apparent discrepancy between the reference in his letter to the “inadequacies” of the deputy chiefs’ performance, and praise that Abraira had for them only one week after the bombings.

In an e-mail sent on April 22 to Fire Department personnel that was obtained by the Globe, Abraira wrote that “every member, from firefighter to Deputy Chief, took effective actions that are now being viewed as a model for response around the country.”

Ciavarra said Thursday that he was speaking generally in his letter when he mentioned the deputy chiefs’ inadequacies, and not about their response to the bombings.

“There is no question that the department, as well as all of the first responders, were outstanding,” Ciavarra said in an e-mail.

He added, “My letter was not an evaluation of the deputies or intended to reflect either my or Chief Abraira’s opinions of their overall performance. It was a private letter expressing our concern about their past conduct and urging them to act responsibly going forward.”

City Councilor Michael P. Ross, a mayoral candidate and chairman of the Public Safety Committee, which is holding the June 18 hearing, said on Thursday that he was “a little bit surprised” by the letter from Abraira's lawyer.

“High ranking fire officials have raised legitimate policy concerns that need to be vetted in an open and transparent forum for the benefit of the public,” Ross said.

Press aides to Mayor Thomas M. Menino did not return messages seeking comment on Thursday. Menino has said that Abraira will “have a future” for as long as he remains mayor.

Boston Fire Commissioner Roderick Fraser, who appointed Abraira in November 2011, declined to comment on the letter from Abraira’s lawyer but said he approves of the chief’s job performance.

In a related matter, Donnellan, the deputy chiefs’ lawyer, said his clients are trying to determine if there is a link between new protocols laying out a reduced roll for the Boston Fire Department in fires at Logan and the deputies’ dispute with Abraira.

Donahue said Thursday in an interview that the changes, which call for more personnel from departments in other cities to respond to Logan, were implemented shortly before the bombings and intended to quicken the response time of assisting units, among other upgrades.