Officials said turnout had been high, although opposition parties disagreed
People in Ethiopia have voted in the first elections since 2005, when polls were followed by violent protests and the arrest of most opposition leaders.
The elections covered nearly 4 million positions, from local councils to many of the seats in parliament won by the opposition in 2005 but never taken up.
Prime Minister Meles Zenawi's EPRDF coalition is expected to win, with its candidates unopposed in many places.
Opposition parties had complained of harassment and intimidation.
Last week, US-based Human Rights Watch said thousands of opposition candidates and prospective voters had been threatened, attacked and arrested during campaigning.
Further elections will be held on 20 April.
State radio said voters lined up peacefully from dawn to cast ballots in Sunday's elections, and Ethiopia's National Electoral Board said it had received no reports of irregularities or incidents before polls closed at 1800 (1500 GMT).
An electoral board official, Tesfaye Mengesha, said it did not yet have an official turnout figure, but estimated it would be about 90% of the 26m registered voters.
But the leader of the opposition Oromo Federalist Democratic Movement (OFDP), Bulcha Demeksa, said there had been a very low turnout.
"There is no interest," he told the Reuters news agency. "This is very far from democracy."
Mr Bulcha said his party had only been able to put forward 2% of the 6,000 candidates it wanted to because they had been threatened government supporters.
The United Ethiopian Democratic Forces opposition party said that of its 20,000 candidates who attempted to register, only 10,000 succeeded.
And only 6,000 of those actually had their names placed on the lists at polling stations.
The run-up to this election has been less lively than in 2005
The BBC's Elizabeth Blunt in Addis Ababa says these elections are almost certain to consolidate the Ethiopian People's Revolutionary Democratic Front's hold on power.
From a staggering total of 3.79m candidates for offices at all levels, all but a few thousand support the government, she says. In many rural councils, whole slates of EPRDF candidates stood completely unopposed.
In the last elections in 2005, candidates fighting under the banner of the Coalition for Unity and Democracy (CUD) won a landslide victory in Addis Ababa, but the polls were followed by violent protests.
The CUD's leaders were arrested and have spent most of the intervening period in jail. Though now free, they were unable to register a party in time for Sunday's elections.