House lawmakers removed a provision banning civil unions from the proposed amendment this week. That change threatens to push back a statewide referendum on the issue until 2016.
Pence also said he is done talking about gay marriage until the General Assembly ends its 2014 session in mid-March.
The proposed ban is being taken up in the Senate in the coming weeks.
Republican Senate President Pro Tem David Long declined Thursday to say whether he supported restoring the civil unions ban.
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