Ethiopian police have arrested five suspects linked to the grenade attack that killed six people in Jijiga, capital of the eastern Somali region.
The suspects are allegedly linked to Eritrea, Ethiopian News Agency reports.
Eyewitnesses told the BBC children and the elderly were killed during a stampede when police opened fire after the blasts on Monday.
The government blames the Ogaden National Liberation Front (ONLF) rebels for the attack. They deny the claim.
OGADEN NATIONAL LIBERATION FRONT (ONLF)
Want Somali-speaking region to break away from Ethiopia
Founded in 1984
Has been accused of bomb attacks in Somali region and the capital, Addis Ababa
Fought major battles with Ethiopian government in 2006
Tension has been high in the Somali region since the ONLF killed 74 people in an attack on a Chinese oilfield in the region last month.
Crowds had gathered at the stadium in the regional capital to celebrate a national holiday marking the 1991 overthrow of Ethiopia's former leader Mengistu Haile Mariam.
At least 45 people were injured in the twin grenade attacks in Jijiga.
Regional President Abdullahi Hassan, who was speaking at the event, was one of the injured, government spokesman Bereket Simon said.
The ONLF says it is not their policy to target civilians.
Ethiopia has long accused its neighbour Eritrea of training and arming the ONLF rebels - a claim Eritrea denies.
The two countries fought a border war in the late 1990s in which tens of thousands of people were killed.