Wilfredo Lee/AP Melanie Alenier, right, speaks as her partner Vanessa Alenier looks on during a news conference, Tuesday, Jan. 21, 2014 in Miami Beach, Fla.

Six gay couples filed a lawsuit Tuesday in Florida seeking to overturn the state's ban on same-sex marriage — joining dozens of other court cases across the country filed since an historic Supreme Court decision last year in favor of LGBT rights.

In the lawsuit, filed in Florida State Court, lawyers from the Equality Florida Institute argue that the state’s constitutional amendment blocking the couples right to marry denies them and their families “the fundamental rights, dignity, and equality guaranteed to all persons by the United States Constitution.”

"Florida is our home, it is where we are raising our child, and where we want to get married," Catherina Pareto, who, along with her partner, Karla Arguello, is one of the couples challenging the ban, said in a statement. "We want to build our lives together, provide a safe and caring home for our child, and share in the responsibilities and protections of marriage."

The lawsuit challenging Florida’s constitutional amendment denying same-sex marriage — which voters approved in 2008 — comes two weeks after the Supreme Court ordered a stay on gay marriage in Utah ahead of an upcoming court challenge in a federal appeals court.

Though more than 30 state marriage bans remain on the books nationwide, gay marriage supporters saw 2013 as a watershed year: If the Utah ruling stands, the number of states that allow gays and lesbians to wed will be 18, up from nine states, plus the District of Columbia last January. And popular support has grown for same-sex marriage nationally, with 54 percent of Americans supporting it in a July 2013 Gallup poll.

Supporters of the right of gays and lesbians to wed have filed 35 lawsuits in 19 states targeting state-level marriage bans, mostly after the Supreme Court decision striking down part of a federal law denying recognition of same-sex marriages.

At least one of the challenges is expected to make it to the Supreme Court, experts said.

How has the striking down of DOMA's Section 3 impacted your relationship? Share your story with reporter Miranda Leitsinger at miranda.leitsinger@nbcuni.com