Attorney Paul Mello argued during an appeal hearing that a U.S. law governing prison litigation "was intended to limit federal court intrusion into state prison systems."
A three-judge panel of the 9th U.S. Circuit Court of Appeals took the case under consideration after a 40-minute hearing and will issue a written ruling later.
Schwarzenegger is appealing a ruling in which U.S. District Judge Thelton Henderson of San Francisco refused in March to terminate the receivership.
Henderson said he had no confidence that improvements in prison health care would continue if he returned control of the medical system to the state.
Henderson ordered the receivership in 2005 after concluding that inadequate health care in the state's severely overcrowded prisons violated minimum constitutional standards, with one prisoner dying unnecessarily each week.
Lawyers for the governor contend that health care has improved and that spending plans by the current receiver, law professor Clark Kelso of Sacramento, are excessive.
But Rebekah Evenson, a lawyer for prisoners who filed a civil rights lawsuit seeking better health care in 2001, argued, "Prisoners are suffering and continuing to suffer for lack of care."
Attorneys for Kelso maintain the receivership is legal under the U.S. Prison Litigation Reform Act and that the state endorsed it by cooperating with the receiver in previous years.