Klaus Hinderer, a police spokesman, said a search of Kretschmer's computer had shown no trace of his having made the chat room posting.
Father under spotlight
Prosecutors indicated that the teenager's father could face legal action if he were found to have violated the country's gun laws, which were tightened in 2002 after 19-year-old Robert Steinhauser shot dead 16 people, mainly teachers, and himself at a high school in the eastern German city of Erfurt.
Kretschmer's rampage was also carried out at a high school.
He returned to his former school on Wednesday to kill nine students and three teachers before fleeing on foot and by car, killing three more people, and eventually turning the gun on himself after a shootout with police.
Kretschmer shot many of his victims in the head at close range with his father's legally-registered 9-mm Beretta pistol.
The father, a member of a shooting club, had 4,600 rounds of ammunition and 15 guns at home, 14 of which were locked in a gun-closet as required by German law.
But the Beretta was kept in the father's bedroom, police said.
"Everything here points to negligence on the part of the father as far as the storage of this weapon is concerned," Ralf Michelfelder, a police spokesman, said.
|Germany toughened its gun laws after a similar school shooting incident in 2002 [EPA]
Students, staff and residents gathered outside Albertville high school in the town of Winnenden, near Stuttgart on Thursday to remember those killed in the rampage.
Kristin Puengel, 14, said a friend of hers was among the students killed.
"I don't know if I can stay at this school," she said. "Every time you enter, the memories come back."
Puengel said she only knew Kretschmer by sight.
"He was somewhat withdrawn, but I would never have thought [he would be capable] of anything like this," she said.