The leader of a leading organization representing gay, lesbian and transgender military service members says he's "cautiously optimistic" about comments made by Jeb Bush regarding transgender people serving in uniform.

Campaigning in Iowa on Wednesday, the former Florida governor was asked by a reporter whether he would support allowing transgender people to serve in the military.

"I’m sure there’s a role for everybody to play in the armed forces. I think it would depend on the specific role and whether it’s appropriate enough," he said. "The first priority for the military is to create an environment where the morale is high, where people are trained and we have the best fighting force. And if you can accommodate that in that kind of environment, I don’t think there’s a problem for it."

He added, however, that he had no specific knowledge of transgender people seeking to enter the military or attempts to block them from doing so.

Gay rights groups have focused on ensuring that transgender individuals can also serve ever since the military's "don't ask, don't tell" ban on gay men and lesbians serving in uniform was repealed in 2011.

An estimated 15,500 transgender people serve in the military, according to the Williams Institute, a legal think tank that studies sexual-orientation and gender-identity issues. The Pentagon has been grappling with how to allow them to continue serving without affecting the morale and cohesion of military units -- a key area of concern in the years leading up to the repeal of the gay ban.

OutServe-SLDN, a military gay rights group, remains one of the leading organizations pushing for changes. In response to Bush's comments, Matt Thorn, the groups' interim director, said that the issue "should and has been a non-partisan issue. While I welcome Governor Bush's statement on open transgender service, I remain cautiously optimistic."

"I hope that all the presidential candidates, the current administration and [Defense] Secretary [Ashton] Carter embrace full LGBT equality in the military," he added. "But they need to listen to the momentum that is happening in the current climate of the era. Transgender servicemembers cannot afford to wait for piece meal policies. Strong and decisive action is needed now."