A security chief said his forces had killed 41 men and captured 36 more over the past five days while they were crossing the border into Ethiopia's Somali state.
"We are still chasing the remaining ones," Jemiel Hajji Mohammed, the chief security officer for Ethiopia's Somali state, said on Saturday.
He added that hundreds of firearms had been recovered from the fighters.
Mohammed said the insurgents were allied to two groups from neighbouring Somalia: Al-Ittihad, a religious group based in Somalia, and the National Liberation Front (ONLF), which is based in southeastern Ethiopia.
According to Mohammed, the captured insurgents all claimed they were trained by Eritrea, a country that fought a two-year border war with Ethiopia that started in 1998 and claimed tens of thousands of lives on both sides.