The two parties are running virtually neck-and-neck. With 66 of the 210 parliamentary seats counted so far, the MDC has reportedly won 35, while Zanu-PF was trailing slightly with 31 seats.
Delays in issuing the results from Saturday's polls have led to further accusations by the opposition that Robert Mugabe, the country's president, has attempted to rig the vote.
The election commission is yet to announce any results in the race for the presidency.
However, the MDC announced its own tally and claimed on Monday that its results, based on counts posted at polling stations in 128 of the country's 210 parliamentary districts, showed it was leading presidential elections....
The Zimbabwe Election Support Network (ZESN) said that according to data it collected from a representative random sample of 435 polling stations across 10 provinces, Tsvangirai was projected to get the highest number of votes followed by Mugabe - with Makoni coming a distant third.
Departure from past
Some election observers have said that initial results were known by 11pm (2100 GMT) on Saturday night, just four hours after polls closed.
In previous elections, partial results have been announced within hours of voting ending.
Notable early results included defeat for Patrick Chinamasa, Mugabe's outgoing justice minister, in the rural eastern constituency of Makoni central.
The MDC also won the first seat to be declared, the newly-formed constituency of Chegutu West, to the west of Harare.