A security chief said his forces had killed 41 men and captured 36 more over the past five days while they were trying to infiltrate the (Ethiopian) state (of Somalia).
"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.
Tension between the two neighbours has risen in recent weeks.
"All the captured insurgents have confirmed they were in Eritrean training camps, trained and armed by the regime and transported by Eritrean planes to Dusamarbeer in Somalia," Mohammed said.
"They tried to infiltrate on Monday, but were spotted by the defence forces"
Jemiel Hajji Mohammed,
chief security officer
From the town of Dusamarbeer the insurgents were ferried to Shilabo on the Ethiopia-Somalia border, about 1750km southeast of the Ethiopian capital Addis Ababa, he said.
"They tried to infiltrate on Monday, but were spotted by the defence forces," Mohammed said, adding: "When they were asked to surrender peacefully, they instead engaged the defence forces."
He added that the security forces are still engaged in mopping-up operations and that the number of dead could increase.
It was not clear whether the Ethiopian army also suffered casualities. Among the arms recovered were Kalashnikov rifles, machine guns and hand grenades, Mohammed said.