PROVIDENCE — The fate of gay marriage legislation in Rhode Island could hinge on the exemptions it affords religious groups that oppose it, the state Senate president said Friday, a day after the House overwhelmingly passed the bill.

Teresa Paiva Weed said she remains opposed to the bill and has heard that the sticking point for many senators is on how broad will be a religious exemption in the measure. Rhode Island is the only New England state that does not allow same-sex marriage.