Protests began last Monday following weeks of opposition charges that the ruling Ethiopian People's Revolutionary Democratic Front (EPRDF) intimidated voters and rigged last month's elections.
A security crackdown led to violence when police and security forces fired into crowds of stone-throwing protestors on Wednesday, killing at least 26 people.
The streets in Addis Ababa were quiet on Sunday, with few shops open and some taxis touting for business.
"Anything that creates the possibility of disturbance of any kind is obviously detrimental," said Berhanu Nega, deputy chairman of the opposition Coalition for Unity and Democracy (CUD).
"Going back to work would contribute to social calm that is needed," he told a news conference.
The appeal came after Information Minister Bereket Simon said CUD leaders had rejected a deal on Friday which called on the opposition and ruling party not to incite violence and to support the work of the electoral commission.
Prime Minister Meles Zenawi accused the CUD of orchestrating the civil disobedience, telling Reuters on Friday he would consider extending a month-long ban on demonstrations and other "preventative" measures to curb further unrest.
The CUD has consistently denied inciting unrest in the capital, which early election results indicate they had won in an unprecedented clean sweep.
Berhanu said CUD leader Hailu Shawel remained under house arrest for the second day.
Millions voted in the May 15 polls, only the second real multi-party contest in Africa's top coffee producer, where many among the population of 72 million suffer recurrent famine.
- Reuters - Thomson Reuters Foundation
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