Robert Mugabe's party has lost its parliamentary majority for the first time since independence in 1980.
Mr Mugabe's Zanu-PF party took 97 of the 210 seats, while the opposition MDC won 99, final official results showed.
Presidential election results have yet to be declared, but the MDC said its leader had won the election. Zanu-PF said this was "wishful thinking".
Mr Mugabe has no intention of leaving Zimbabwe, his country's ambassador to the UN told the BBC.
"Robert Mugabe is Zimbabwean," said Boniface Chidyausiku. "He has lived his life to work for Zimbabwe. Why should he choose another country?"
He said Mr Mugabe still had work to do to end economic hardship which he said had been caused by external forces.
'Anxiety and disappointment'
The BBC's Grant Ferrett in Johannesburg says that although the release of parliamentary results by the Zimbabwe Election Commission is significant, the main power in Zimbabwe lies with the president.
The MDC released its own results to back up its claim of victory in the presidential poll.
MDC Party Secretary General Tendai Biti said its leader Morgan Tsvangirai had won 50.3% of the vote to President Robert Mugabe's 43.8%, so avoiding a presidential run-off.
In his news conference, Mr Biti said there was "anxiety and disappointment" at the failure of the Zimbabwe Election Commission to declare presidential results.
But Mr Biti said that if the election commission decided that neither of the main candidates had won outright, the MDC would be prepared to take part in a second round.
For Zanu-PF, Deputy Information Minister Bright Matonga said the claim of victory was irresponsible and could incite violence.
And, interviewed by the BBC, he said the pattern of results from the parliamentary election suggested that there would be a second round in the presidential election.
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The root cause of all Zimbabwe's teething problems is Mugabe's failure to hold free and fair elections
Asked if Mr Mugabe would take part he said: "Only the top two go for a run-off, he cannot bring in another candidate to replace another, which means that President Mugabe and Mr Tsvangirai will go for the run-off if there is going to be a run-off."
Mr Matonga added that the delay in officially declaring the result was due to the complexity of the process, with 75% of voters living in rural areas.
Despite the MDC's declaration, the issue of whether Mr Tsvangirai has won more than 50% remains in dispute.
The Zimbabwe Election Support Network, a coalition of civil society organisations, said earlier that he had won 49% to Mr Mugabe's 42%.
It based its results on a random sample of polling stations - where results were posted following the polls.
In Cape Town, South Africa's Archbishop Desmond Tutu said President Mugabe should have retired long ago.
"If he had stepped down 10 or so years ago, he would be held in very, very high regard," said the Nobel laureate.
"We must honour him for the things that he did do... We hope he will be able to step down gracefully, with dignity."
In a separate development, a senior Zanu-PF official has told a BBC correspondent in Zimbabwe that he believes Mr Mugabe has been fatally damaged.
ELECTION RESULTS FROM MDC
The official, who did not want to be identified, said that by not declaring victory on Sunday or Monday, Mr Mugabe had shown weakness.
Now, he told our correspondent, civil servants and police were determined to show even-handedness in their treatment of the Zanu-PF and the opposition.
Zanu-PF has also rejected suggestions that talks have been taking place with the MDC on a possibly handover of power.
MDC sources had earlier told the BBC that the outline of an agreement had nearly been reached for Mr Mugabe to leave office.
Trained as a teacher
1961: Married Ghanaian Sally Hayfron
1964: Imprisoned by Rhodesian government
1980: Wins post-independence elections
1980s: Accusations of atrocities in south-west
1996: Marries Grace Marufu
2000: Loses referendum
2000: Land invasions start
2002: Wins presidential elections, dismissed by western observers
2008: Runs for a sixth term as president
In his first public appearance since the election, Mr Tsvangirai told a news conference on Tuesday evening there was "no way the MDC will enter in any deal before ZEC has actually announced the result".
United Nations Secretary General Ban Ki-moon appealed for calm.
He urged the "utmost transparency be exercised so that the people of Zimbabwe can have full confidence in the process".
The White House said it was clear the people of Zimbabwe had "voted for change".
UK Prime Minister Gordon Brown called for the results of the presidential election to be published as soon as possible.
Mr Mugabe, 84, has not been seen in public since the election but Mr Matonga has denied rumours the president had left the country.
He came to power 28 years ago at independence but in recent years Zimbabwe has been plagued by the world's highest inflation, as well as acute food and fuel shortages.