Ethiopia's government has insisted the country is stable following the death of long-time Prime Minister Meles Zenawi at the age of 57.
Mr Meles died at a hospital in the Belgian capital Brussels late on Monday after a long illness.
His body has been flown back to the capital Addis Ababa and a period of national mourning has been announced.
Large crowds carrying candles ran alongside the hearse as it travelled through the city on Tuesday, the BBC reports.
State media reported that Deputy Prime Minister Hailemariam Desalegn would take over until elections in 2015.
Mr Meles' death has sparked fears of a leadership vacuum, Kenyan Prime Minister Raila Odinga among those expressing concern the prime minister's death could herald a period of instability for Ethiopia.
He told the BBC the situation in Ethiopia was "very fragile" and that he was unsure whether the country was "sufficiently prepared for his succession".