A proposal backed by Mayor Bloomberg to expand protections for unmarried victims of domestic violence would open the Family Court system to individuals in same-sex relationships seeking protection from an abusive partner.

Under a bill that will be introduced in the City Council next week, victims abused by a domestic partner or live-in girlfriend or boyfriend would be allowed to seek a civil order of protection from a Family Court. State law currently allows victims of domestic violence to seek protection in Family Court if they are married to, divorced from, related by blood to, or a parent to the same child as the abuser.

“It’s a misconception to think that domestic violence only affects women and only occurs between a husband and wife,” Mr. Bloomberg said yesterday. “Actually this is a crime that occurs between people in all types of domestic, intimate relationships, but for far too long the law has not provided them all with the same critical protections.”

Proponents of the bill say Family Court is often a preferred option for domestic violence victims because it does not initially require a criminal proceeding and can be useful in de-escalating violent behavior by requiring a perpetrator to enroll in a program for batterers, for example.

The speaker of the City Council, Christine Quinn, who is supporting the bill, said domestic violence is just as prevalent in gay and lesbian relationships as in heterosexual ones.

Ms. Quinn, who is openly gay, is the former executive director of the New York City Gay and Lesbian Anti-Violence Project, which works with victims of domestic violence. She said it is unfair that same-sex couples are held to a different standard than married couples.

“We will continue to advocate on the state level for a broader definition of family, but we can’t wait for the state to act,” she said. Ms. Quinn is disclosing her state agenda later this month, which is expected to state the council’s support for same-sex marriage. Susan Sommer, a senior counsel at Lambda Legal, a national civil rights organization advocating for gay rights, said the bill would help remedy an area of society in which protections and rights are tied to marital status while marriage is withheld from same-sex couples.

She said the measure would help the gay rights movement because it acknowledges there are many kinds of relationships and families in New York and “helps to illustrate the irrationality of hinging important protections around a marital status.”

It is unclear how many people would take advantage of the access to Family Court, if the bill were to be approved, a city official said. The police commissioner, Raymond Kelly, said police officers responded to more than 200,000 domestic violence calls last year and made more than 5,000 arrests for domestic violence.

Mr. Bloomberg said domestic violence crime fell by 32% between 2001 and 2007, and domestic violence-related homicides fell by nearly 40% during that same period.