Wednesday night's vote for the largely symbolic measure was 5-1 with two abstentions.
Santa Fe Mayor David Coss was a sponsor of the measure.
Council members who abstained or voted "no" say the city has no authority to make law on same-sex marriage and claim the issue has divided or polarized residents.
City Attorney Geno Zamora recently provided the council with an opinion saying state law doesn't define marriage as between a man and a woman and that same-sex unions are legal.
New Mexico Attorney General Gary King is in the process of coming up with an opinion on the subject, which hasn't been adjudicated with finality in the state's court system.