President Robert Mugabe's ruling Zanu-PF party has been defeated by Zimbabwe's combined opposition.
The electoral commission said with all but seven seats declared from 207 contested, the main opposition Movement for Democratic Change (MDC) won 96 seats, a breakaway MDC faction 9 seats, and the ZANU-PF 94. One seat was taken by an independent.
Official results from the presidential election, also held on March 29, have yet to be published.
But the MDC claims its leader Morgan Tsvangirai has beaten Robert Mugabe.
The party has released its own results from the weekend polls and said Mr Tsvangirai has won 50.3 per cent of the votes compared to 43.8 per cent for Mr Mugabe.
But Mr Mugabe's Zanu-PF party dismissed the claims as "wishful" with deputy information minister Bright Matonga saying: "President Mugabe is going nowhere. We are not going to be pressurised into anything."
Mr Tsvangirai said earlier: "Our country is on a precipice, on a cliff edge, and we await with great anxiety and apprehension, the confirmation of the people's will. Today we face a new challenge, that of governance. That of rehabilitating our beloved country."
"Today we face the challenge of bringing everyone together and restructuring a fabric that will clothe and cover everyone of us without regard to race, colour, party affiliation, tribe, religion, age and sex.
"The challenge of giving birth to a new Zimbabwe, founded on restoration and not on retribution, on equality and not discrimination, on love not war, on tolerance not hate."
Mr Mugabe, described by critics as a dictator and tyrant, has been in power since the country won its independence from Britain 28 years ago.
Reports that Mr Tsvangirai has already been holding handover talks with him have been dismissed by the MDC leader who said he was waiting on an official announcement of election results before he would enter any discussions.
Mr Tsvangirai said: "There are no discussions. Let's wait for Zimbabwe Electoral Commission to complete its work, then we can discuss the circumstances that will affect the people."
In London, Prime Minister Gordon Brown said in a statement: "I'm very concerned about the delay in the publication of the election results; after all, this is an election that took place last weekend.
"It's very important that the election results are published as soon as possible, that there is no further delay.
"The world is watching Zimbabwe. We will be vigilant in what we do and, of course, what we want to see is that the whole of the Zimbabwean people can be guaranteed that the elections are fair and are seen to be fair and we get the democratic outcome that the people of Zimbabwe have chosen.
"That's what we're looking for and that's what we want to happen as soon as possible."
And Foreign Secretary David Miliband said that conditions for free and fair elections were "not in place" ahead of the elections and must be improved if a second round of voting is called.
