The city council in the southern Arizona community of Bisbee will rewrite a recently enacted civil-unions ordinance after being threatened with a lawsuit by the state attorney general’s office, which said the ordinance ran afoul of a state ban on same-sex marriage.

The council voted Thursday night to withdraw the ordinance so it can be revised to take out language that drew objections from social conservatives and Attorney General Tom Horne. The wording concerned community property, inheritances, appointment of guardians and disposition of remains after death.

“To the extent that we can . . . tighten the language, we’re hoping that we can do that and we can move forward quickly,” Mayor Adriana Badal said Friday.

A spokeswoman for Horne said the council’s decision likely means that a lawsuit expected to be filed next week won’t be necessary.

The ordinance, passed last week, made Bisbee the first Arizona city to legalize civil unions for same-sex couples.