The Congolese Rally for Democracy (RCD), whose presidential candidate is Azarias Ruberwa, a former rebel leader, said in a statement: "These irregularities are so significant that they distort the results of the vote across the national territory."
The counting of millions of ballots cast in Sunday's election is still under way.
It was the first free multi-party election in 40 years in the war-scarred Democratic Republic of Congo.
Thousands of UN peacekeepers had protected voting across the vast, former Belgian colony.
The RCD's fraud allegation posed an early headache for electoral authorities and the UN, which are trying to ensure that disputes over the results do not lead to a divisive political crisis.
Election officials have appealed for people not to make premature victory claims before official results due by August 20.
In its complaint, the RCD cited cases of ballot-stuffing and biased election officials.
It said Rwandan Hutu rebels had interfered in voting to favour Joseph Kabila, the president, who is widely viewed as favourite to win the elections.
It also complained of widespread duplication of voting cards and accused Kabila's party of handing out money to voters to persuade them to back him.
Ruberwa said that if these violations were not rectified, his party reserved the right to challenge the electoral process through legal channels or "democratic means".