The Movement for Democratic Change (MDC) claims the poll on July 31 was a “farce” riddled with fraud and voters were allegedly intimidated by Mr Mugabe’s ZANU-PF party.
Lawyers for the MDC have lodged papers with the constitutional court in the capital Harare arguing the result was rigged, should be annulled and a new election held.
Zimbabwe’s electoral commission had declared veteran politician Mr Mugabe the winner with 61% of the votes in the presidential election, against MDC leader Morgan Tsvangirai with 34%.
“We want a fresh election within 60 days. The prayer that we also seek is to declare the election null and void,” MDC spokesman Douglas Mwonzora told journalists outside the court.
Zimbabwe’s constitution says the court must rule on the case within 14 days.
Most analysts believe the MDC’s legal challenge to Mr Mugabe’s victory will not be successful given ZANU-PF’s dominance over the judiciary and state institutions in the country.
Mr Mugabe, who has been president since 1987, will be sworn in only after the case is decided.
ZANU-PF has denied any vote-rigging in the election, which Mr Tsvangirai, who has served as Mugabe’s prime minister in a fractious unity government, has called a “coup by ballot”.
Election observers from the African Union and the Southern African Development Community broadly approved the presidential and parliamentary elections as orderly and free.
But the vote result has been questioned by the West.
The United States, which maintains sanctions against Mr Mugabe, has said it does not believe his re-election was credible.
The European Union, which has been looking at easing sanctions, has also expressed concerns over alleged serious flaws in the vote.