© Marco Ugarte /The Associated PressWearng a Guy Fawkes mask, a protester holds a banner that reads in Spanish, "No to another fraud," during a march in Mexico City on Saturday.
The demonstrators, including students, leftists, anarchists and union members, shouted slogans criticizing Pena Nieto's Institutional Revolutionary Party, or PRI, and the electoral authority.
Pena Nieto won Sunday's election by almost 7 percentage points, according to the official count, returning the PRI to presidential power after 12 years in the wilderness.
The PRI previously ruled Mexico for seven decades, during which time it was accused of rigging elections and repressing protesters.
"The PRI threatens many people and buys others with a couple of tacos," said Manuel Ocegueda, a 43-year-old shop worker participating in the march.
Pena Nieto is due to take power in December, replacing Felipe Calderon of the conservative National Action Party, or PAN.
The constitution barred Calderon from running for a second term. The PAN candidate, Josefina Vazquez Mota, finished third, with many voters dissatisfied over relentless drug violence and sluggish growth.
Leftist Andres Manuel Lopez Obrador finished in second place, but has refused to concede, accusing Pena Nieto of stealing the presidency.
Pena Nieto denies any wrongdoing and PRI officials say they could sue Lopez Obrador over the accusations.
Lopez Obrador was runner-up as well in the 2006 presidential race, but by a much closer margin, after which he also said there had been fraud and led major protests.
He has so far stayed away from protests this year, but said he was collecting evidence of fraud to give to officials.
On Saturday, Lopez Obrador called on the PAN to join forces with him to file a legal challenge to the election.
Mexico's electoral tribunal has until September to evaluate any complaints and officially name Pena Nieto as the next Mexican president.
Pena Nieto, 45, a former state governor, promises to reform Mexico's oil industry and labor laws to kick-start growth and boost security spending to reduce the country's high murder rate.
Calderon has congratulated Pena Nieto on his electoral victory, along with dozens of world leaders.
...by showing a few guys with Anonymous masks and not publishing long shots of the demonstrations that would allow us to see how big they are.
But you can get an idea from the little video included here. Mexico City is a BIG city, and that street appeared to be filled with people for many blocks. They say "thousands." Well, how many thousands? A hundred thousand? A thousand thousand? We can't tell from these stories how many people realize they are being tricked.