It is one of the state’s most contentious issues and has become a major issue in presidential politics.
The state’s supreme court ruled in June that a man’s polygamous marriage could not be recognised under state law.
But Texas Attorney General Greg Abbott has argued that a ban on same-sex marriage is unconstitutional and a violation of the US Constitution.
He has called for the state to “exercise its sovereign power” to ban polygamous unions, a view backed up by the state solicitor general, who has called it “a religious issue” and “unconstitutional”.
“The federal government has not been clear about what it is, where it comes from, and what it means to have a marriage between a man and a woman,” Attorney General Ken Paxton said.
“We are going to be asking the Supreme Court to clarify that.”
The US Supreme Court ruled in May that the US government had the authority to define marriage as a union between a woman and a man.
“That’s the kind of power the state has and the kind the federal government lacks,” Paxton told CNN.
“If the federal courts decide that this is an issue that we are going in this direction, then we’re going to pursue that.”
The Supreme Court has repeatedly ruled in favour of same-gender marriage, with five justices saying the ban was unconstitutional.
A legal fight that could last years The case is the latest in a long line of challenges to the US constitution.
In 2013, the Supreme, a conservative court in the US, struck down the federal Defense of Marriage Act (DOMA), which denied same-age military marriages to same- sex couples.
In the same year, a federal judge in Utah ruled that a state’s ban on gay marriage violated the 14th Amendment, which guarantees equal protection under the law.
But in June 2016, the US Supreme court ruled against a federal law that would have allowed same- gender marriage.
That ruling was followed by a flurry of lawsuits, many of them challenging the constitutionality of the same- marriage ban.
The Texas case was filed on behalf of a man who says he married a man after having been married twice.
Under the Texas law, it would be possible for a same-gendered marriage to be recognised in Texas, but the same could not occur in a state that does not recognise the marriage.
In Texas, there are five states where same- and opposite-sex couples can marry.
The state is a stronghold for the far right in Texas politics, which is dominated by a coalition of evangelical Christians and conservative Christian activists.
The group FreedomWorks is also a major supporter of the Republican candidate for governor in Texas and the Republican presidential candidates.
Mr Abbott said in a statement that the decision by the supreme court is “a huge blow to the constitutional fabric of the United States”.
A petition to the supreme courts of Texas, Florida, Maryland and Minnesota was signed by more than 1.2 million people on Tuesday.
It is the second time in a year that the high court has ruled in favor of gay marriage.
A ruling by the court in April ruled that Texas had no legal authority to ban gay marriage and a lower court had already struck down a similar ban.
“The Supreme Court of Texas has confirmed that the Texas Legislature has no constitutional right to exclude same- or opposite-gender couples from marriage, and has struck down any attempts to enforce the ban,” the group said in its petition.