The parties are alleging that the numbers presented by the national electoral commission do not match theirs.
Civil society groups are backing their position and say they have also collated evidence of irregularities, which they allege played a part in the resounding 71.84% victory of the ruling MPLA.
Although the MPLA's victory is not disputed, there are claims that tens of thousands of voters in opposition stronghold areas were prevented from casting their ballots because of confusion over voter lists.
This week, Isaías Samakuva, the leader of Unita – the MPLA's former civil war enemy – published what he said was clear proof that the election was rigged and named several senior MPLA members and a group of Chinese nationals whom he said were involved in the alleged fraud.
Describing the situation as a "national emergency", Samakuva said: "The results of this election are flawed, because they come from a rigged process that was neither free nor democratically exercised."
Unequal, unfair and disloyal
Earlier, Unita said: "The election was an unequal, unfair and disloyal competition in which the … people were the main victims of a fraud."
As well as questioning the results tabulated by the electoral commission and voters' access to the ballot boxes, Unita has also hit out at the unfair access to state media afforded to the ruling party and the use of government resources to pay for MPLA campaign events.
Under the terms of Angola's new Constitution, the MPLA's win of 175 parliamentary seats out of 220 hands President José Eduardo dos Santos, who has been in power for 33 years, a new five-year term.
Unita won 18.66% of the vote, giving it 32 seats. In third place was the newly formed Casa-CE, with 6% and eight seats.
The PRS scored 1.7% and three seats and the FNLA, with 1.13%, won two seats.
Late on Wednesday the electoral commission rejected the opposition parties' complaints, saying they were "in bad faith", "without evidence" and "out of context". Unita, Casa-CE and the FNLA had 48 hours from that time to submit their appeal to the Constitutional Court.
The court said on Wednesday that it would be open through the weekend to accept any legal challenges from opposition parties, but a "final and non-appealable" decision would be made by September 17, a national holiday commemorating the birth of liberation president Agostinho Neto.
But Angelo Kapwatcha, from the Civil Society Electoral Process Reflection, a group of politically non-aligned national observers, told the Mail & Guardian that few people had faith in the Constitutional Court.
"The court is officially supposed to be independent, but its judges are personally appointed by the president and we have never known it to deliver a judgment that goes against the ruling party.
"We have evidence of multiple irregularities during this election and it will be a real test for the court to see how they react to this challenge."
Kapwatcha said it was hard to know how opposition parties, their followers and society in general would react if the complaints were rejected, but he could not rule out street demonstrations.
Samakuva said his party would fight to prove the result was "fraudulent" by exercising all possible legal avenues, including going to international bodies, but also by using the Angolan constitutional right to public demonstration.
Many Angolans – and international investors – wait nervously to see the outcome of the opposition challenge. The contested result in 1992 between the MPLA and Unita led to a new phase in the country's long civil war.
With the country at peace for more than a decade, there is no expectation of mass violence. But there is a new air of unpredictability, although it is one that has largely been ignored by the MPLA, which continues to celebrate its victory with street parties and saccharine newspaper tributes to Dos Santos.