BERLIN — After days of confusion, German authorities said on Friday that they had concluded that contaminated sprouts from an organic farm in the country’s north were the most likely cause of one of the world’s worst outbreaks of E. coli.

Officials acknowledged, however, that laboratory tests to confirm the findings had produced only negative results and that questions remained about how the sprouts had been contaminated in the first place.

To reach their conclusion, health officials said they relied on an epidemiological study of the pattern of infection among patients, tracking the outbreak along the food chain, from hospital beds to restaurants and back to the farm, southeast of Hamburg, at Bienenbüttel.

Hours after the announcement in Berlin, officials in a different region, North Rhine-Westphalia, said they had, for the first time, identified the pathogens thought to be causing the outbreak in an open package of bean sprouts from the same farm.