The 25-year-old Mijailo Mijailovic last week had confessed to fatally stabbing Lindh, one of the country's most popular politicians, in September 2003.
"One can see from the very violence, the power in his attack, that he intended to kill Anna Lindh," chief prosecutor Krister Peterson said on Monday, disputing claims by Mijailovic's lawyers that the attack was not premeditated.
"He knew that it was Anna Lindh whom he was attacking," chief investigator Leif Jennekvist said.
Lindh, one of Sweden's most popular politicians, was stabbed last September while shopping for clothes in a Stockholm department store.
The chief investigator said Mijailovic "rushed up to her, took out a knife and stabbed her… in the middle of her body."
Lindh died of her wounds later in the hospital.
Released transcripts from police interrogations of Mijailovic showed him claiming hearing voices that urged him to attack Lindh.
"I think it was Jesus, that he has chosen me," said Mijailovic on being grilled whose voice he had heard.
Mijailovic goes on trial on Wednesday and faces between 10 years and life in prison if convicted for murder.