Kentucky Governor Steve Beshear, a Democrat, argues in a brief filed Thursday that the state's ban on gay marriage promotes Kentucky's “legitimate societal and economic interests in natural procreation.”

A federal lawsuit challenging the state's ban is currently before the Sixth Circuit Court of Appeals in Cincinnati, which will hear arguments on Wednesday along with cases from 3 other states.

(Related: Opponents call for 4 days of prayer to ask 6th Circuit to uphold marriage bans in 4 states.)

In a 12-page brief filed in Love v. Beshear, the governor cites a recent dissent in a case challenging Virginia's ban to argue that its ban “does not violate the Equal Protection Clause” of the 14th Amendment.

On Monday, the Fourth Circuit Court of Appeals in Richmond upheld a lower court's decision invalidating Virginia's ban.

In his dissent, Circuit Judge Paul V. Niemeyer chided the majority for failing “to explain how this new notion became incorporated into the traditional definition of marriage except by linguistic manipulation.”

(Related: Appeals court strikes down Virginia's gay marriage ban.)

“Although indirect, such [marriage] benefits are clearly subsidies that come at a cost to the Commonwealth. … Under Johnson, the Commonwealth is not obligated to similarly subsidize same-sex marriage, since doing so would not possibly further its interest,” Beshear's hired counsel quoted from Niemeyer's dissent.

“Therefore, just as providing veterans' educational benefits to conscientious objectors would not have furthered Congress's legitimate interest in encouraging voluntary enlistment, so would providing marriage benefits to same-sex couples not promote Kentucky's legitimate societal and economic interests in natural procreation. Thus, excluding same-sex couples from the state marriage benefit does not violate the Equal Protection Clause,” the brief states.

Beshear is defending the state's ban in two cases before the Sixth Circuit.

(Related: Opposition to gay marriage in Kentucky drops 22 points over 10 years.)

(Brief provided by Equality Case Files.)