..."We have won this election," said the secretary general of the Movement for Democratic Change (MDC), Tendai Biti. "This trend is irreversible."
BBC Southern Africa correspondent Peter Biles says the MDC's claims are based on partial, unofficial results.
The more slowly-counted votes from the rural areas, where President Mugabe has always had majority support, may decide the final outcome.
BBC contributors say opposition activists have been celebrating in the towns of Bulawayo, Mutare and Masvingo.
The elections will no doubt be free and fair. The allegations being peddled are unfounded
But Zimbabwe's chief elections officer expressed concern "that some stakeholders have gone on to announce purported results... when in fact the results are being verified and collated".
The MDC says the commission was appointed by Mr Mugabe and is not to be trusted...