The 33-year-old is accused of orchestrating the death of his 28-year-old Indo-Swedish wife, Anni, who was shot as the couple travelled in a taxi in Cape Town back in November 2010.
He is being treated at a hospital in his home city of Bristol and has been excused from attending the hearing at Westminster Magistrates' Court.
"We suggest that the evidence shows that there has been a significant improvement....There are more positive observations about how he wishes to return to fight the case against him," barrister Hugo Keith, on behalf of the South African government, told the court at the start of the five-day extradition hearing.
Shrien Dewani's father Prakash and brother Preyen were also present in court.
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The accused is being treated for post-traumatic stress disorder (PTSD) and depression at a mental hospital in Bristol and his lawyers have reported fluctuations in the state of his mental health.
They have previously claimed that he would be a high suicide risk if extradited, and his human rights may be violated due to the risk of being violently attacked.
The court heard that Dewani's depression is now moderate rather than severe and he is suffering from PTSD "considerably less" than before.
South African authorities have offered assurances that Dewani would be kept in a single cell if he returns, and therefore would be at less risk of attack.
They have also said that if he was found to be mentally ill, he would be admitted to a psychiatric hospital there.
In April, prosecutors said his condition had improved "significantly", but in May, the court was told he had suffered a relapse.
A judge must now decide if Shrien Dewani's mental health has improved sufficiently for him to be extradited or whether conditions in South African detention centres might breach his human rights given his current health.