(CNN) -- The official ballot count in Mexico's presidential elections began on Wednesday, as the presumptive president-elect sought to consolidate his victory while one challenger refused to concede.

Enrique Peña Nieto received the most votes, according to preliminary results released the night of Sunday's balloting, and according to a quick count released by the Federal Election Institute, known by its Spanish acronym IFE. The quick count gives Peña Nieto a margin of victory ranging from 6.07 to 7.65 percentage points.

But Andres Manuel Lopez Obrador, the candidate for a progressive coalition, says he has evidence of irregularities at a majority of polling places and wants a full recount.

The counting process that started Wednesday is designed to double-check all the election returns recorded in each district and can carry out recounts in certain cases.

The IFE says a final count election result will be available by Sunday.

Officials have called this election the most transparent in Mexico's history. It was the first election in which scanned copies of district-by-district election returns were posted on the Internet.

But there is no shortage of accusations of electoral manipulation by Peña Nieto's party, the Institutional Revolutionary Party, or PRI.

The party, which was in power for 71 years before being voted out in 2000, was known for being corrupt and authoritarian. Its apparent victory marked a triumphant return of the party after 12 years.

But supporters for Lopez Obrador say the PRI resorted to its old ways of corruption, too.

Daniel Avila, a representative for the anti-Peña Nieto student movement #YoSoy132 (I am 132), told CNN en Español that his group had already received 1,100 complaints of alleged vote buying, stuffed ballot boxes and intimidation.

The group has photos, video and audio proof of these violations, the group claims.

"What we're going to try to do is find all these people to get testimonies, and then take that evidence to the IFE," Avila said.

One sign that Lopez Obrador supporters pointed to were the long lines that were reported at the Soriana chain of supermarkets. Voters flocked to the stores to use gift cards handed out by the PRI in exchange for votes, some allege.

The electoral authorities should question the owners of the chain, said Irma Erendira Sandoval, a political analyst at the National Autonomous University of Mexico.

The beginning of Wednesday's count marks the beginning of clarifying whether there was fraud, she said.

"This is a fundamental stage where the transparency and cleanliness of the entire election is at stake," she told CNN en Español.

According to the group Alianza Civica, which took a poll with what they said was a representative sample, nearly 30% of voters reported being exposed to at least one example of vote-buying or coercion.

Taking advantage of the fact that the individual election returns are available online, critics began circulating copies of suspicious returns.

One such document that is being shared by PRI opponents is an electoral return from a district in Michoacan, which appears to show that 362 of 732 registered voters cast ballots, but that somehow the PRI won 945 votes.

For his part, Peña Nieto, in an interview with "NewsHour" on PBS, praised Mexico's democratic system and put his trust in the electoral authorities.

"We have electoral tribunals that will be responsible for addressing these issues and attending to these complaints, the ones filed by candidate Lopez Obrador," he said.

The presumptive president-elect said he is not worried about his legitimacy as Mexico's next leader, given the gap between the top two finishers.

"With this new trust from the Mexican people, without a doubt our capacity to prove ourselves will be tested," Peña Nieto said.

Under the law, ballots will be recounted in cases where the difference between the top two finishers is 1 percentage point or less, and when the number of annulled votes is greater than the difference between the top two.

Lopez Obrador must wait until Sunday to formally submit any application for a recount to the Federal Election Tribunal.

Avila, the youth activist, said he realizes that Peña Nieto will almost certainly be confirmed as president, and he contended the PRI's alleged maneuverings sealed it.

"The amount of evidence we present does not matter. It is a fact that Enrique Peña Nieto will remain," he said. "We have had a position since before the election that this was being imposed by fraud, and it's what we've been seeing."