Officials begin counting ballots at a voting station in Chinamhora, near Harare, late Saturday.
1 of 4 Sunday's announcement sets up a showdown with Zimbabwe's government, which will release the results of its count on Monday.
Leaders of the opposition Movement for Democratic Change (MDC) have already dismissed the government's results -- expected to show a victory for President Robert Mugabe -- as rigged in favor of the incumbent leader.
There are concerns that if each side claims victory, tensions could ignite and violence could erupt.
At a news conference in Zimbabwe's capital, Harare, MDC leaders said their candidate Morgan Tsvangirai has won 67 percent of the vote, based on one-third of the returns, journalists inside Zimbabwe told CNN.
The party did not explain how it arrived at those results. Watch polls close in Zimbabwe. »
The Zimbabwean government has denied CNN and other international news organizations permission to enter the country to report on the elections. Read about reporting on the elections.
MDC Secretary-General Tenda Biti has accused the ruling Zanu-PF party of chasing its party's agents away from polling stations.
One of Mugabe's challengers, his former finance minister, Simba Makoni, who was expelled from the Zanu-PF after announcing his bid to unseat Mugabe, said it was "premature to judge that the environment before the balloting has had some impediment."
Journalists reported high turnout in Saturday's vote, which critics of the government predicted would be rigged or marred by fraud.
The bombing happened early Saturday, and it was not immediately clear whether it was connected to the elections, police said. No one was inside the home at the time.
The United States this week warned of a possible unfair election, and New York-based Human Rights Watch announced earlier this month that the elections were likely to be "deeply flawed."
The elections presented one of the toughest challenges to Mugabe, who has ruled the country for nearly three decades. Watch report on Mugabe's 28 years in charge of Zimbabwe. »
A hero of the country's civil war against the white Rhodesian government, Mugabe became the country's first black prime minister in 1980. But nearly three decades later, he has consolidated his rule over all aspects of Zimbabwean life, and the country does not appear better for it.
His country was once revered for offering its citizens some of the best education and health care in Africa, but now, schooling is a luxury and Zimbabwe has one of the lowest life expectancies in the world.
Zimbabwe was once known as the breadbasket of southern Africa, but now it is difficult to get even basic food supplies. Inflation has skyrocketed to more than 100,000 percent while food production and agricultural exports have dropped drastically. Watch reasons for meltdown of Zimbabwe's economy »
Part of the economic freefall is traced to Mugabe's land redistribution policies, including his controversial seizure of commercially white-owned farms in 2000. Mugabe gave the land to black Zimbabweans who he said were cheated under colonialist rule, and white farmers who resisted were jailed.
In 2005, Mugabe launched Operation Clean Out the Trash, in which he razed slum areas across the country.
Mugabe denies mismanagement and blames his country's woes on the West, saying that sanctions have harmed the economy. E-mail to a friend
CNN's Robyn Curnow in Beitbridge, South Africa, contributed to this report