Despite the opposition gaining seats, CNRP President Sam Rainsy, 64, said the government of the Cambodian People's Party has until the end of August to sort out voting irregularities.
Rainsy asked why more than a million eligible voters were unable to cast their ballots.
"The CNRP doesn't recognize the result announced by the ruling CPP or the very similar National Election Commission results," Rainsy told reporters at his headquarters in Phnom Penh.
"The information the CNRP has received so far isn't acceptable," he said.
"Fifteen percent of voters -- about 1.3 million -- were unable to vote because of [voting] list irregularities. There also were about 1 million ghost names on the voter list and about 200,000 duplicate names."
Cambodian Prime Minister Hun Sen, 60, in power for 28 years, won another five-year term, but the party's grip on the National Assembly was weakened considerably.
The CPP won 68 of the 123 seats in Sunday's elections, 22 fewer seats than it picked up in 2008. The Post said the CPP's royalist coalition partners failed to win any seats.
The CNRP won the remaining 55 seats.
The CNRP's rejection comes as people rioted in the streets of one area of the capital, overturning a car and starting it on fire on Sunday during voting hours, the Post reported.
Residents and would-be voters took to the streets of Phnom Penh's Stung Meanchey district over concerns about alleged ballot fraud and names left off the voter list.
A mob detained the polling station director inside the pagoda, according to the district governor.
Some 100 riot police confronted the rioters who pelted officers with stones, but no deaths or serious injuries were reported.
Elections have been held in Cambodia since the 1990s. Prior to that the country was ravaged by wars followed by four years genocide from 1975 to 1979 under the brutal Khmer Rouge rule, which was overthrown with the backing of Vietnam.
The genocide is estimated to have claimed nearly 2 million lives, dramatically portrayed in the movie "Killing Fields."
The ruling CPP has much support in the countryside, partly because of improved economic growth among the rural poor after the devastation wrought by the Khmer Rouge in the 1970s, the BBC reported.
Younger urban voters looking for a break with the past likely backed the opposition and Rainsy, who recently returned to Cambodia from self-imposed exile.
But Rainsy, French-educated and a former investment manager in French financial companies, was ineligible to run in the election.
In 2010 he was sentenced in absentia to 11 years in prison on charges he says were politically motivated.
But analysts say his return to Cambodia July 19 -- after a royal pardon was issued at Hun Sen's request -- seems to have helped his party's cause, the BBC said.
Upon his return, tens of thousands of people greeted Rainsy at the airport and along a route to a park where he spoke to supporters, Time magazine reported at the time.
"I have returned to rescue the country," he said.
Rainsy was convicted of racial incitement and destruction of property and spent the past four years living in exile until a royal pardon led to his return as head of the Cambodia National Rescue Party.
Hun Sen faced pressure from the international community to allow a free and fair election, but allowing his rival's return puzzled observers, Time said.
"I think we're entering a new phase in Cambodian history," Rainsy told Time by phone. "It's the beginning of something like the Arab Spring."
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