A spokeswoman for Patrick said the governor was not available for comment Wednesday night but would speak to reporters Thursday.
Earlier this month, US District Court Judge Mark Wolf ruled that Kosilek, who identified himself Robert Kosilek when he strangled Cheryl McCaul in 1990, is entitled to the surgery because it is the only adequate care for her gender identity disorder.
Under Globe policy, Kosilek is being referred to as a woman because that is the gender with which she identifies.
A lawyer for Michelle Kosilek, Frances S. Cohen, declined to comment on Wednesday because she had not been informed of the state's decision.
McCaul's niece, Laura J. Brandel, 41, of Plymouth, said in a phone interview that she was pleased to learn of the appeal. "I hope that it leads to something good, because he deserves nothing," Brandel said of her aunt's killer. "This whole thing is just a joke and a nightmare, that's what it is. Everybody focuses so much on Robert; and it's a male, it's not a female, I don't care what it calls itself. My aunt was a beautiful woman, and she didn't get a say in anything."
Brandel added, "He robbed her of her life, and now he expects that he's going to get a brand new life. It's absurd."
Kosilek, now in her early 60s, was born Robert Kosilek, but by 1990 was transitioning to a female identity. She strangled McCaul in Mansfield that year.
Kosilek has been staying in a men's prison in Norfolk while taking hormones and developing female physical qualities.
In a statement, Gunner Scott, executive director of the Massachusetts Transgender Political Coalition, criticized the state's decision to appeal.
"Care that is medically necessary for prisoners cannot be denied based on public opinion," Scott said.
Jennifer Levi, director of the Transgender Rights Project at Gay & Lesbian Advocates & Defenders, added in the same statement, "Constitutional rights belong to everyone, even the least loved, least popular people among us. Prisoners have a right to necessary medical care, and this is indisputably medical care, as the very strong district court decision established."
The state Department of Correction's own doctors have said that surgery is the only appropriate care for Kosilek, who has attempted self-castration as well as suicide.
In his ruling, Wolf said he expected the department to follow the same standards of care that it would for any illness. The cost of the surgery ranges from $7,000 to more than $50,000, according to informational surgery and transgender websites.
State Senator Bruce Tarr, a Gloucester Republican and the senate minority leader, said Wednesday in a statement that he welcomed the appeal.
"The Department of Correction is to be commended for standing up and opposing this outrageous request and for taking the necessary action to prevent it from being legitimized by a legal decision," he said.