Oklahoma Gov. Mary Fallin declined Tuesday to act on South Carolina’s extradition warrant for Dusten Brown until the birth father of Veronica has a chance to challenge the legality of his arrest for failing to turn her over to her adoptive parents on James Island.

Fallin said she had received Gov. Nikki Haley’s signed warrant seeking Brown’s extradition to South Carolina and had spoken to her counterpart in the Palmetto State. But Fallin said in a statement she has declined Haley’s request to sign the warrant until Brown has a chance to contest the action at a Sept. 12 court hearing in Sequoyah County, Okla.

“This is a difficult and sad situation for everyone involved, and Gov. Haley is working with law enforcement, the state of Oklahoma, and the family to resolve it as quickly as legally possible,” said Doug Mayer, Haley’s spokesman, by email in response. “Regardless of the varying personal opinions on this case, it is every governor’s first priority to uphold the rule of law and that is what must happen here. Both the U.S. and South Carolina Supreme Courts have spoken and the governor remains committed to returning baby Veronica back home safely.”

Brown is wanted in Charleston County on a custodial-interference charge for failing to surrender his 3-year-old daughter to Matt and Melanie Capobianco. He surrendered to Oklahoma authorities on Monday but was quickly released on a $10,000 bond. South Carolina authorities are now trying to get him back in custody and sent to South Carolina.

The Capobiancos, expressing frustration at the delay in reuniting with Veronica, vowed Monday to travel to Oklahoma and retrieve the little girl, whom they described as a “captive.” Word surfaced late Tuesday that they had indeed traveled to the Sooner State and planned to hold a press conference in Tulsa this morning.

A statement from Fallin’s office said she “believes that Mr. Brown should have the opportunity to argue his case in a court of law, and she will not act on the rendition order before that date. However, the governor encourages both the Capobianco family and Mr. Brown to reach a resolution outside of court as quickly as possible.”

Fallin said that as a mother, her heart goes out to Veronica, “who has been placed in a terrible situation.” She said she can also imagine the pain both sides in the case are feeling, but her hope is “that sending Mr. Brown to face criminal charges in South Carolina is unnecessary.”

“To be clear, the legal system cannot deliver a happy ending in this case. Only Mr. Brown and the Capobianco family can do that,” she said. “For Veronica’s sake, I urge them to reconcile and to come to an agreement that best serves their child and grants all parties some measure of peace.”

After the Oklahoma governor’s statement, the attorney for Christy Maldonado, Veronica’s birth mother, thanked Fallin “for her concern and her acknowledgement of her duty to uphold the law.”

The attorney, Lori Alvino McGill, referred to Fallin’s suggestion that the opponents in the dispute resolve their differences. But Alvino McGill said Brown should start with “a small measure of kindness” by letting the Capobiancos visit or speak with Veronica.

“No one wants to see Mr. Brown go to jail — least of all the Capobiancos,” who want Brown and the Cherokee culture to be a part of Veronica’s life, the attorney said. “But everyone has to follow the law, including Mr. Brown.”

Brown’s attorney, Clark Brewster, told the Tulsa World newspaper on Monday that Brown will fight extradition.

“I suspect that’s going to be a serious challenge of whether that’s a crime in this state,” Brewster told the newspaper. “That’s a very unusual statute in South Carolina. We’ll argue that it’s not an extraditable charge.”

Charleston County Sheriff’s Maj. Jim Brady and 9th Circuit Solicitor Scarlett Wilson said they had no new information to provide about efforts to bring Brown and Veronica back to South Carolina.

Meanwhile, attorneys for Brown Wednesday will challenge a judge’s request for them to reveal Veronica’s whereabouts and what they knew about their client’s resistance to an order finalizing her adoption. The hearing takes place at 3 p.m. in Charleston County Family Court.

Family Court Judge Daniel Martin approved the adoption on July 31. But after the toddler and Dusten Brown didn’t show up for a visitation with the girl’s adoptive parents, he ordered Brown’s attorneys to hand over the information.

Brown’s representatives have said he missed the visitation because he was attending required training in Iowa with the Oklahoma National Guard, of which he is a part-time member.

The order is one of the strongest actions in the custody dispute since the U.S. Supreme Court ruled in June that Brown wrongly got custody of the girl under the Indian Child Welfare Act. Brown and Veronica are members of the Cherokee Nation.

After the case was sent back to South Carolina courts, the Capobiancos’ adoption was finalized.

The girl, who turns 4 next month, lived with the couple for the first 27 months of her life and has been living with Brown in the 19 months since.

Andrew Knapp contributed to this report.