Dewani, 34, wearing a dark suit and tie, made a brief appearance before Cape Judge President John Hlophe for a pre-trial conference.
Dewani's mental condition has improved since he has been receiving treatment at Valkenberg Psychiatric Hospital, the Western Cape High Court heard.
"I am informed that he has been fully co-operative and that his condition has improved," Dewani's lawyer lawyer Francois van Zyl told the court.
"I've been informed that he has been fully co-operative and that his condition has improved. We have been told by the treating psychiatrist not to consult with him for more than 30 minutes and even that proved frustrating because he can't even concentrate for 30 minutes," Van Zyl was quoted as saying by Independent Online.
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The judge ordered Dewani to appear in court again on June 20. Western Cape Director of Public Prosecutions Rodney de Kock agreed to the postponement.
Dewani appeared to have lost weight since his last court appearance. He seemed bewildered and confused as Judge President Hlophe addressed him and his eyes scanned those present.
The courtroom was packed to capacity with members of the public, a large media contingent and members of the ANC Women's League, who called for justice for the victim.
Sitting directly in front of the dock were his brother and parents.
Dewani is charged with the November 2010 murder of his bride Anni while they were on honeymoon in Cape Town.
He is charged with conspiracy to commit kidnapping, robbery with aggravating circumstances, murder, kidnapping, and defeating the ends of justice.
Dewani claimed he and his wife were kidnapped at gunpoint as they drove through Gugulethu in Cape Town.
He was released unharmed, but his wife's body was found in the abandoned car the next day.
Dewani was brought to South Africa a month ago after fighting extradition for three years, claiming that he has severe depression and Post Traumatic Stress Disorder.
He is being voluntarily detained at Valkenberg Hospital under 24-hour police guard.