Oklahoma's Republican governor, attorney general and other elected officials blasted the ruling. Kern immediately stayed the effects of his ruling, anticipating an appeal.
Alliance's brief Monday said that, over time, marriage would lose its distinction as the place where heterosexual couples traditionally have children and instead be regarded as merely an option.
"Without the stability that marriage provides, more man-woman couples would end their relationships before their children are grown ... and more children would be raised outside a stable family unit led by their married mother and father," the group wrote, predicting an increase in the divorce rate.
Byron Babione, senior counsel for Alliance Defending Freedom, said 76 percent of Oklahoma voters expressed what they thought was best for children and society, referring to the amendment vote.
"Marriage expresses the reality that men and women bring distinct, irreplaceable gifts to family life, especially for children who deserve both a mom and a dad," Babione said in a statement Monday night.
Kern's ruling was one of several in the past few months to strike down or void part of such a ban.
A similar appeal out of Utah is being heard by the 10th Circuit. Utah state attorneys filed their opening arguments earlier this month, saying the optimal environment for raising a child is with a mother and father. A federal judge there had ruled in December that the voter-approved ban was unconstitutional. More than 1,000 gay couples got married in Utah before the U.S. Supreme Court granted a stay in the case, halting the marriages during the appeals process. Oral arguments in the Utah case are scheduled for April 10.