HARRISBURG — Attorney General Kathleen Kane is firing back at Gov. Tom Corbett over the defense of Pennsylvania’s law that effectively bans same-sex marriage and said it isn’t the governor’s job to tell the attorney general what the office’s duties and obligations are.

The dispatch, in a letter that emerged Wednesday, was the latest biting exchange between Kane, a newly elected Democrat, and Corbett, the Republican former attorney general whom she heavily criticized during her campaign.

In the letter sent Tuesday, Kane’s chief of staff, Adrian King, called Pennsylvania’s marriage law “one of the last discriminatory statutes” in Pennsylvania and predicted it will be struck down by the courts.

“Just as discriminatory laws based on race, religion, gender, disability and ethnic origin have been struck down by the courts one by one, so too will the marriage law,” King wrote to Corbett’s lawyer James Schultz. “In short, this is a watershed moment.”

Two days after Pennsylvania’s marriage law was challenged in federal court, Kane, who supports same-sex marriage, said she believed it to be unconstitutional and could not ethically defend it. The statement drew applause from Democrats and proponents of same-sex marriage, but Corbett, the Republican Party and other opponents of same-sex marriage criticized her as shirking her duty to defend state laws.

Pennsylvania is the only northeastern state that doesn’t allow same-sex marriage or civil unions. A 1996 state law defines marriage as a civil contract in which a man and a woman take each other as husband and wife.

On Tuesday, Corbett’s office said it would defend the law and in a letter to King, Schultz wrote that the law leaves Kane no choice but to defend the ban.

“Nothing excuses the attorney general from undertaking her legal duty to defend the statute challenged” by the lawsuit, Schultz wrote.