Long, R-Fort Wayne, and Bosma, R-Indianapolis, said they still support the amendment and believe it will win approval from lawmakers and voters, but they are wary of taking on the issue before the U.S. Supreme Court rules on related cases this summer.
Social conservatives in the House and Senate had pressed them to tackle the issue this year.
The first case before the Supreme Court involves California's constitutional amendment that forbids same-sex marriage. The second concerns a federal law that denies gay couples who legally marry the right to obtain federal benefits available to heterosexual married couples.
Gay marriage is currently allowed in nine states — Connecticut, Iowa, Maine, Maryland, Massachusetts, New Hampshire, New York, Vermont, and Washington— and the District of Columbia.
Indiana lawmakers approved the constitutional ban in 2011 despite arguments from opponents that it was unnecessary because state law already limits marriage to being between one man and one woman. Supporters of writing the ban into the Indiana Constitution have said a judge could approve gay marriage by overturning state law.
Under the state's constitutional amendment process, lawmakers have until next year to consider putting the marriage ban before voters. The measure must pass the Legislature again before it can be put on a ballot.