Tens of thousands of Ethiopians have marched in a government-supported rally against the killing of Ethiopian Christians in Libya, but some demonstrators directed their anger at the authorities, prompting clashes with the police.

Wednesday's march at Addis Ababa's Meskel Square turned violent as stone-throwing protesters clashed with the police, who used tear gas against the crowd and arrested at least 100 people.

"We are tired of speeches and propaganda! We want action! Revenge for our brothers!" shouted a group of youths, referring to Ethiopians seen apparently being beheaded or shot in a video released on Sunday by the Islamic State of Iraq and the Levant (ISIL) in Libya.

"Ethiopia sent troops to Somalia, Liberia, Burundi, but the government is not capable of protecting its own citizens!" shouted one protester, referring to its peacekeeping roles in the African Union and United Nations.

Ahaza Kassaye, the mother of one of the victims identified as Eyasu Yikunoamlak, told the AP news agency during the protest that she was overwhelmed by the massive turnout.

"I'm happy now. I'm very happy. I was just mourning the death of my son with family members and my neighbours. I never expected this to happen," she said.

Read/watch more: Ethiopia mourns Christian nationals killed by ISIL

Kassaye, who had to seek shelter in a cafe when the protest turned violent, said she hoped the government would react to the killings by closing all illegal border crossings and arresting suspected human traffickers.

The Ethiopian victims are believed to have been captured in Libya while trying to reach Europe.

Government response

Ethiopian legislators on Tuesday were debating a possible response to the ISIL killings, but it remains unclear if military action is an option.

Three days of national mourning began on Tuesday over the killings.

The government has promised to help repatriate migrants who are still in Libya and has warned its citizens not to go to areas where ISIL is active.

The rally came a month before Ethiopia holds parliamentary elections, the first since the death of long-time leader Meles Zenawi.

Current Prime Minister Hailemariam Desalegn faces little, if any, opposition challenge.