Dewani, 32, is being treated at a secure mental hospital and claimed in July that he needed a year to be treated for depression before he could face extradition over the death of his Swedish wife Anni in 2010.
But his psychiatrist now believes Dewani’s mental health has “materially improved”, a hearing at Westminster Magistrates Court heard on Tuesday.
“It is now to be described as moderate rather than severe,” Hugo Keith, barrister for the South African government, told the court.
“He still suffers however from severe Post Traumatic Stress Disorder,” he added.
Dewani, who denies any involvement in his wife’s killing, was taken to a psychiatric hospital in April 2011 over fears he could commit suicide.
His 28-year-old wife was shot dead when the taxi she and Dewani were travelling in was hijacked in Cape Town’s Gugulethu township.
Two South African men have so far admitted their role in the murder and claim businessman Dewani orchestrated the killing.
Mziwamadoda Qwabe was jailed for 25 years and taxi driver Zola Tongo for 18 years, saying Dewani offered 15,000 rand ($1,800) to arrange the killing and make it look like a carjacking.
Dewani is currently being treated at a secure mental health facility in Bristol, southwest England, where he is subject to a curfew and must be accompanied by a member of staff when he goes out.
But his psychiatrist now believes Dewani’s mental health is stable enough for him to move from the clinic to an open rehabilitation ward, Keith told the court.
The case was adjourned for a further hearing on October 2. An application to alter his bail conditions may be heard on October 12.