The unrest ignited in cities across the Oromia region that is home to many of Jawar's supporters.
At least six people were killed on Wednesday, regional officials in Oromia told local media outlets.
But the real death toll could be in the "dozens," a local official in the regional capital, Adama, told the AP on Thursday, speaking on condition of anonymity because he was not authorized to talk to the media. Several Oromia residents told the AP that non-Oromos had been attacked, with their properties looted and burned.
Jawar said he was surprised by Abiy's remarks.
"We have a very cordial relationship but we have differences, too, so I do criticize him," Jawar said, adding he is willing to sit down and talk with the prime minister. "It was him who convinced me to have government security, saying my security was not an individual one but national security. Now I don't know what happened."
The head of the federal police, Endeshaw Tassew, said no measure was taken by the government or police forces against Jawar. "His message was wrong," he said, but he confirmed the government was removing security details for some people due to what he called the improving security situation in the country.