Some people died in a panicked stampede after police employed tear gas and baton charges, they said.
Thousands had gathered for a religious festival in Bishoftu, 40km (25 miles) from the capital Addis Ababa.
Some reports said police responded after anti-government protesters threw stones and bottles. Others said demonstrators were entirely peaceful.
Ethiopia's government said in a statement that "lives were lost", adding: "Those responsible will face justice".
An Oromo activist, Jawar Mohamed, is quoted as saying nearly 300 people were killed and many more injured. He said troops and a helicopter gunship had opened fire, driving people off a cliff and into a lake.