State legislators voted Wednesday to hold a constitutional convention next month to debate a proposed amendment that would replace same-sex marriage in Massachusetts with Vermont-style civil unions.

House and Senate members have already given initial approval to the amendment, but the state constitution requires them to approve identical language in two successive sessions before the amendment can be put before state voters.

The Supreme Judicial Court legalized same-sex marriage in Massachusetts in 2003, making it the only state where such unions are legal. Foes then backed a constitutional amendment that would outlaw gay marriage but permit civil unions.

Civil unions would provide same-sex partners the same legal benefits without the status of marriage.

Legislative approval of the amendment has been thrown into doubt after some supporters in the initial vote announced they had changed their mind. The most recent is Rep. Anthony Petruccelli, a Democrat, who was quoted this week in Bay Windows as saying he will not vote for the proposal despite supporting it last year.

The motion to reconvene the legislature as a constitutional convention Sept. 14 passed on a voice vote.

In June, the Massachusetts Family Institute submitted a citizen's initiative petition that would amend the constitution to define marriage as between a man and a woman.

Gov. Mitt Romney withdrew his support for a compromise and is backing the initiative petition. He said the compromise "muddied" the issue of gay marriage by legalizing civil unions.