About 200 people have been killed in the protests since November, Human Rights Watch (HRW) said.
The unrest began over government plans to expand the capital's administrative control into the region.
The government later dropped the plan, but protesters dismissed the decision as "too little too late".
Oromia is Ethiopia's largest region, surrounding the capital, Addis Ababa.
Many people in the region complain of being politically and economically marginalised in a country where the Ethiopian People's Revolutionary Democratic Front (EPRDF) coalition has ruled since 1991.
New York-based HRW said, in a report, that anti-government protests had decreased in the last few weeks, but the "crackdown continues".
"Almost daily accounts of killings and arbitrary arrests have been reported to Human Rights Watch since 2016 began," it added.
HRW said thousands of people had been detained without charge since November.
But Ethiopia's Communications Minister, Getachew Reda, told the BBC that it was a "stroke of magic" for HRW to release a report "from half way across the world".
He acknowledged that there had been trouble, but said attacks on public buildings were carried out by armed gangs "who are trying to stir up emotions in the public".
Mr Getachew said that HRW has been "churning out report after report" on Ethiopia without a presence in the country, and its allegations against the security forces were an "absolute lie".
At the last census in 2007, the Oromo made up Ethiopia's biggest ethnic group, at about 25 million people out of a population at the time of nearly 74 million.

The police ombudsman confirmed that the spray was used during the parade on the Ormeau Road on Tuesday evening.
The PSNI said two officers received minor injuries during a "minor disturbance". A 26-year-old man has been charged with assault.
The parade's organiser said children suffered swollen eyes and lips.
Noel Liggett told Good Morning Ulster said the CS spray was "indiscriminately" used after police confronted the parade.
He said police believed cars were being damaged as the parade made its way up the road, an allegation he described as "completely false".
"Around 20 children were on parade with us yesterday, the average age would be six, seven, eight and nine. Around that age group," he said.
"I was quite shocked to see many young children in a state of shock.
"Five of them had suffered the effect of CS gas and a number of young children in the band had also suffered the effects of the gas."
Mr Liggett said a "very frank meeting where both sides put their case" was held with police after the parade and that he would "question the common sense" of police.
"The police knew this was a parade for juniors, there was a lot of young children in the area," he said.
Writing on Twitter, Mrs Foster said she would be meeting senior police over the incident.
Police said a PSNI motorcycle had also been damaged in the incident.
A man will appear at Belfast Magistrates Court on Tuesday, 26 April charged with disorderly behaviour and two counts of assault on police.
Ethiopia has dismissed allegations it is violently suppressing protests in its restive Oromia region as an "absolute lie".
[NEXT_CONCEPT]
First Minister Arlene Foster has said she has spoken to the chief constable after police used CS spray during a junior Orange Order parade in Belfast.