House Speaker Brian Bosma and Senate President Pro Tem David Long said Thursday that their respective caucuses decided the issue should wait until the 2014 session.
Long and Bosma have said they are apprehensive of taking on the issue before the Supreme Court rules on related cases this summer. Social conservatives in the House and Senate had pressed them to tackle the issue this year.
Lawmakers approved the constitutional ban in 2011 but must approve it again before the end of next year in order to amend it into the constitution. The measure would then go on a ballot to give voters final say.