Texas' top law officer has called the US Supreme Court decision legalising gay marriage in all 50 states a "lawless ruling" and vowed to support state workers who refuse to marry couples on religious grounds.
The court ruled on Friday that marriage for all is a constitutional right.
Texas Attorney General Ken Paxton said clerks could be fined if they refuse to issue marriage licences.
However, he said that his office would defend them in court free of charge.
Despite the landmark ruling, opponents of gay marriage are preparing for more legal challenges. Many want to protect the interests of people with religious objections to the unions.
"This newly minted federal constitutional right to same-sex marriage can and should peaceably coexist with longstanding constitutional and statutory rights, including the rights to free exercise of religion and freedom of speech," Mr Paxton wrote in a memo to state employees.
Many gay couples in Texas have already wed since Friday's ruling. But couples in nearby Mississippi have been blocked from obtaining marriage licences.
Mississippi Attorney General Jim Hood said gay marriage would not be legal in the state until the US 5th Circuit Court of Appeals gives the go-ahead. It is unclear when the court will act.
In Louisiana, an official had said they found nothing in the ruling stating the marriages must be available immediately, but the state began issuing licences on Monday.
"We don't have a choice," Louisiana Governor Bobby Jindal told NBC News on Sunday. "Our agencies will comply with the court order."
Mr Jindal, a Republican who is running for president, also sought to protect religious freedoms after the ruling.
"I think it is wrong for the federal government to force Christian individuals, businesses, pastors, churches to participate in wedding ceremonies that violate our sincerely held religious beliefs," Mr Jindal said.
"We have to stand up and fight for religious liberty. That's where this fight is going," he added.
Gay marriages in the US only apply to secular unions so churches and clergy are not legally required participate.
However, some conservatives say florists, bakers and other businesspeople associated with weddings should not be legally required to serve gay customers if they have religious objections to same-sex marriages.