Officials say it currently seems the 17-year-old did not hold a grudge against the school.
"There are no indications at the moment of any warning of suggestion that the attack could have been foreseen," Baden-Wuerttemburg's Interior Minister Heribert Rech said.
"It is conspicuous that most of his victims were female," he said, but added that he did not want to speculate about possible motives.
Mr Rech described Kretschmer as an unremarkable student who had gained average grades at school and was enrolled on a course to be a salesman.
Some former schoolmates have described him as a shy loner who never had a girlfriend, struggled to fit in and spent all day on his computer.
But one fellow student, Eileen Toramen, said he was a normal guy who had friends, good grades and future prospects.
"He was an average, totally normal guy," she said.
"He didn't really stand out, he wasn't a recluse either. He was totally normal, he was also nice, sweet."
'Panic and shock'
Heribert Rech said it appeared Kretschmer had used a gun registered to his father, a member of a shooting club with a collection of 15 guns.
"But one weapon was not stored in the safe, but was lying at another place, in the bedroom," he told reporters.
The town of Winnenden, along with the rest of the country, is in shock
"So, the young offender must have taken the gun from the bedroom."
The teenager entered the Albertville secondary school, north of Stuttgart, dressed in black combat gear, at 0930 (0830 GMT) on Wednesday.
Eight girls and one boy were killed after he opened fire, along with three teachers, all of them women. Seven other children suffered minor injuries.
According to reports, he returned to one classroom three times. On the last visit, he asked: "Aren't you all dead yet?"
As Kretschmer fired at students, terrified pupils leapt from the school windows to escape.
A student called Celina told the BBC how the gunman had come into her classroom and "just shot everywhere".
"I threw myself on the floor and took my friends with me, and then I went to a corner and put a table in front of me, and he came again a second time and shot again," she said.
"We were in panic and in shock."
Some 60 spent rounds of ammunition were later found in the school.
As he fled the school, the gunman killed a passer-by.
He hijacked a car, taking its driver hostage, before stopping in the town of Wendlingen, about 40km (25 miles) away from the school.
He then shot and killed two men at a car showroom.
A fire-fight with police followed and the teenager was hit in the leg.
He fled and turned the weapon on himself.
Wednesday's attack was the most deadly school-shooting in Germany since 2002, when a former school pupil in the eastern city of Erfurt killed 14 teachers, two pupils and a police officer.
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