The psychiatrists base their conclusions on interviews with Qureshi's ex-wife, who claims that Qureshi beat and raped her over the six months of their marriage before suddenly disappearing back in 2001.
Qureshi, 35, and Yasmin Chaudhry, 28, are on trial for drowning Chaudhry's two-year-old daughter from another relationship by plunging her head into a bucket of water in October 2010.
Qureshi has British and Chaudhry Norwegian citizenship, but both are of Pakistani origin.
The murder took place, according to investigators, after the toddler interrupted the couple during an online video chat via MSN in the early hours of the morning.
The man, who was in London at the time, allegedly told the woman to "discipline" the child and issued instructions which led to Chaudhry plunging the child's head under water until she lost consciousness.
Chaudhry then called emergency services and reported the incident as an accident. The child died in hospital the following day.
Qureshi told the Oslo court at the start of this month that he had been "shocked" when he learned that his lover Yasmin Chaudhry, 28, filled the mouth of her 22-month-old daughter Huaina with chilli, and denied that he had instructed her to discipline the child.
"I thought it was hideous," he said. "It was not a punishment, but because it was funny. The baby made a face and its eyes filled with tears."
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In the interview with the court psychiatrists, however, Qureshi's former wife said that the 35-year-old was a manipulative liar who had taken control of her both physically and mentally, demanding sex up to eight times a day, beating her and raping her.
Qureshi's lawyer contests these claims, while Qureshi told the court that his ex-wife was bitter and wanted to exact revenge for the way he left her in 2001.