The brief statement released by state media on Monday did not say how many seats the governing coalition believed it had won or offer any other details about Sunday’s vote.
But about 90% of the 25 million-strong electorate turned out for polls for what is seen as a test of the Ethiopian government’s commitment to democracy.
Official results are to be announced on 8 June.
The main opposition Coalition for Unity and Democracy – which came into the race with just three of 547 seats in parliament – had been expected to do well in its stronghold of Addis Ababa and other areas.
Opposition leaders had claimed earlier on Monday that, by their count, they had won at least 185 seats across the country, including 23 seats in the capital.
The ruling coalition that ended an oppressive dictatorship in 1991 was expected to move ahead as results come in from rural areas, where most of Ethiopia’s 70 million people live.
As the count proceeded, opposition politicians were toning down earlier complaints of irregularities and sweeping threats to reject the results.
Prime Minister Meles Zenawi’s
The threats had led the prime minister to ban demonstrations and put the capital’s police under his direct command.
At a news conference on Monday, Berhanu Nega, vice-chairman of the Coalition for Unity and Democracy, said it was too early to decide whether to accept the results, though he said reports of wide abuses continued to come in.
International observers – allowed to monitor voting there for the first time – did not back the opposition’s accusations of widespread problems.
Former US President Jimmy Carter, who led 24 teams of observers from his human rights and development centre, said that while there were minor problems in the run-up to the vote, the elections on Sunday were “as good as any we’ve seen”.
More than 500 foreign observers, including European Union teams, monitored the polls.
Hailu Shawel, the leader of the Coalition for Unity and Democracy, scoffed at the observers for their upbeat assessment, calling them “a joke” and saying they had failed to do their duty. But the large turnout indicated most Ethiopians embraced the process as largely free and fair.
Prime Minister Meles Zenawi has pledged his sometimes authoritarian government would introduce greater democracy. Many had pointed to Sunday’s race as a test of his commitment to reform.