The family of Orion Krause, the Oberlin College graduate accused of killing three relatives and a caretaker in Groton last week, expressed gratitude Tuesday for the support they’ve received and offered condolences to the loved ones of the slain health aide.

Attorney Edward W. Wayland, who is defending Krause, 22, released the statement on behalf of his client’s family.

Krause, a resident of Rockport, Maine, is accused of fatally bludgeoning his mother, Elizabeth Krause, 60; her parents, F. Danby Lackey III, 89, and his wife, Elizabeth Lackey, 85; and their caretaker, Bertha Mae Parker, 68.

“Members of the Krause family want to express their deepest sympathies to the family of Bertha Mae Parker,’’ the statement said. “They know too well the pain they are experiencing today.’’

Krause’s relatives also extended thanks to Groton residents and the town’s police department for their “compassion and support.’’ The family has no further comment and wants the media to respect their privacy, the statement said.

Krause was arraigned Monday in Ayer District Court, where he was ordered held without bail and committed to Bridgewater State Hospital so that doctors can evaluate whether he is competent to stand trial.

Krause pleaded not guilty to four counts of murder. The attacks occurred at the home that Krause’s grandparents shared on Common Street in Groton.

The couple and their daughter, Elizabeth Krause, were found dead inside the residence. Parker, a native of Louisiana who recently began working for the Lackeys, was found outside, authorities have said.

Officials have revealed few details about the slayings, which were discovered Friday evening after a neighbor, Wagner Alcocer, alerted police that a young man covered in mud and blood had come to his house, saying he had just murdered four people and needed help.

Krause’s next court hearing was scheduled for Oct. 30.

John Tlumacki of the Globe staff contributed to this report. Laura Crimaldi can be reached at laura.crimaldi@globe.com.