US death row inmate Christa Pike has been discharged from hospital following her botched execution at the end of last month, her lawyers have said.

The 50-year-old murderer has been returned to the prison where she has spent the last 30 years, according to a statement from her lawyers on Saturday.

She is continuing to receive medical care at the prison.

Pike survived two lethal injections of the drug pentobarbital on 30 September, which left her in a critical condition in hospital.

Earlier this week, she regained consciousness and began speaking - stunning experts, medical staff and her lawyers.

"She is grateful to the first responders and her medical team for their care in these extraordinary circumstances," her lawyers said in their statement.

Pike's case is now in uncharted territory as Pike is believed to be the only person to have survived an execution attempt by lethal injection.

At a court hearing on Wednesday, Tennessee Assistant Attorney General Will Ayers told the judge he does not know whether the state intends to reschedule Pike's execution.

The judge also ordered the state of Tennessee to preserve all evidence related to the failed execution. That evidence could lay the groundwork for a future lawsuit against the state.

Pike was 18 when she and her then-boyfriend, Tadaryl Shipp, beat, tortured and killed 19-year-old Colleen Slemmer, whom they had met at a job training camp for low-income young people.

After Pike survived two lethal injections, she lost consciousness and was taken to a local hospital.

She eventually woke up and began talking again on Tuesday - her lawyers said her first words were "Where am I?" and "Who are you?"