BERLIN — Investigators have determined that German-grown vegetable sprouts are the cause of the E. coli outbreak that has killed 29 people and sickened nearly 3,000, the head of Germany’s national disease control center said.

Reinhard Burger, president of the Robert Koch Institute, said even though no tests of the sprouts from an organic farm in Lower Saxony had come back positive for the E. coli strain behind the outbreak, an investigation into the pattern of the outbreak had produced enough evidence to draw the conclusion.

“In this way, it was possible to narrow down epidemiologically the cause of the outbreak of the illness to the consumption of sprouts,” Burger said. “It is the sprouts.”

The breakthrough in the investigation came after a task force from the three institutes linked separate clusters of patients who had fallen sick to 26 restaurants and cafeterias.

“It was like a crime thriller where you have to find the bad guy,” said Helmut Tschiersky-Schoeneburg from the consumer protection agency.

“They even studied the menus, the ingredients, looked at bills and took pictures of the different meals, which they then showed to those who had fallen ill,” said Andreas Hensel, head of the Risk Assessment agency.