Chaney said Bryant may still try to block his efforts to establish the program but noted he had not spoken with the governor.
In a statement late Tuesday, Bryant spokesman Mick Bullock said Bryant wasn't giving up his fight.
"Governor Bryant understands that as a Democrat, General Hood was placed in an extremely difficult position," Bullock said. "Governor Bryant will continue to resist efforts to further implement 'Obamacare,' including a health insurance exchange."
The rift over the health exchange is a rare public dispute between members of the Republican Party, which controls all statewide offices except the attorney general's office.
Chaney's office has been working on an exchange for months, and he has been sharply criticized by tea party conservatives, who believe he is promoting big government.
Chaney disagrees with their criticism, saying exchanges are inevitable and it is in the state's best interest to have as much control as possible.