- Projections indicate Enrique Peña Nieto won more than 37% of votes
- His closest competitor has not conceded saying "the last word has yet to be said"
- Peña Nieto's apparent victory marks a triumphant return to power for his party
- Voters also cast ballots for federal, state and local offices
Follow the Mexican election coverage in Spanish at CNNMéxico.com
Mexico City (CNN) -- Enrique Peña Nieto is the projected winner of Mexico's presidential election, according to a quick count by election officials.
Representative samples from polling stations throughout the country gave Peña Nieto the lead, with between 37.93% and 38.55% of votes, the Federal Election Institute said.
The projected victory for Peña Nieto marks a triumphant return to power for the PRI, which controlled Mexico's presidency for more than 70 years, until the election of the National Action Party's Vicente Fox in 2000.
"I take with great emotion and a great sense of commitment and full responsibility the mandate Mexicans have granted me today," Peña Nieto told supporters, standing at a podium with a sign that said "Mexico won."
Criticisms of Peña Nieto and concerns about the PRI's possible return to power have fueled a student movement that has staged protests throughout the country in recent weeks.
Calderon addresses Mexican citizens 
Young Mexicans vulnerable to crime 
Ghost towns of Mexico's drug war But the charismatic 45-year-old former governor has also galvanized fervent support among residents of his home state and party loyalists nationwide.
Andres Manuel Lopez Obrador, Peña Nieto's closest competitor, said Sunday night that he wasn't ready to concede.
"The last word has yet to be said," the former Mexico City mayor told supporters in the capital late Sunday.
An official individual vote tally begins Wednesday.
Lopez Obrador trailed by 6 percentage points in the Sunday night quick count, which projected he garnered between 30.90% and 31.86% of the vote.
In the 2006 presidential vote, election authorities said Lopez Obrador narrowly lost to Felipe Calderon. Lopez Obrador claimed election fraud and never conceded, referring to himself as "the legitimate president of Mexico."
His supporters protested nationwide. In Mexico City, they staged sit-ins and blockades.
On Wednesday, Lopez Obrador told throngs of supporters in Mexico's capital that he was confident that he would "win the presidency again."
The Consulta Mitofsky, GEA/ISA and Parametria firms also said their exit poll results projected a win for Peña Nieto, with more than 40% of voters saying they cast ballots for the PRI candidate.
Peña Nieto's campaign platform included plans to stop the rise in food prices, promote energy reform, give social security to all Mexicans and reduce violence nationwide.
In addition to Peña Nieto, three other candidates were vying for the presidency in what officials called "the largest and most complex election day" in the country's history.
Ruling party candidate Josefina Vazquez Mota was trailing in exit polls and the quick count projection, which said she received between 25.10% and 26.03% of votes.
As preliminary results trickled in Sunday night, Vazquez Mota acknowledged that the trend did not appear to be in her favor.
Gabriel Quadri of the New Alliance, who lagged far behind in polls before and after the election with less than 3% of votes, praised Mexico's election authorities Sunday night.
"We have very solid, democratic institutions," he said.
In polling centers throughout the country, workers began the day Sunday assembling cardboard voting booths marked with bold black letters saying, "The vote is free and secret."
But some voters said they were afraid of fraud.
From a command center in Mexico's capital, student activists tracked election irregularities reported in local media, and encouraged others to document activities at their neighborhood polling stations.
The monitoring effort was spearheaded by youth who have led a series of social media campaigns and street protests leading up to Sunday's vote.
At the Revolution elementary school near the heart of Mexico City, Martha Rojas Ramos was near the front of the line, waiting for the polls to open Sunday morning.
The 58-year-old flea market merchant, who carried bags of merchandise in her arms as she waited in line to vote before heading to work Sunday morning, said money was tight, and the economy was a key issue for her in this year's election. Peña Nieto, she said, is the right person to solve Mexico's economic problems.
"He is obviously prepared. There was obviously a dirty war against him," said Martha Rojas Ramos, 58.
Critics lamenting the possible return of the PRI to power aren't thinking straight, she said.
"That's all in the past. What's important is that he is young and has all the ability to represent us," she said.
Alejandro Garcia, a 33-year-old accountant, said he supported Peña Nieto's security strategy, which aims to decrease violence in Mexico.
Calderon, Mexico's current president, made combating cartels a top priority when he took office in December 2006. Since then, more than 47,500 people have died in drug-related violence nationwide, according to government statistics.
Garcia said the surge in violence has negatively impacted daily life throughout the country.
"People don't go out as much in the streets. People go inside their homes earlier in the day. ... Now we are seeing things that we didn't see before. Maybe they were going on, but they weren't as open as they are now," he said. "I think (Peña Nieto) is the one to stabilize the country."
Mexicans also cast ballots from beyond the country's borders. On Saturday, election officials said they had received 40,737 absentee ballots from Mexicans living abroad.
Voters elected governors in the states of Chiapas, Guanajuato, Jalisco, Morelos, Tabasco and Yucatan. In Mexico City, the nation's capital, residents elected a new mayor.
Online and on the streets, Mexico youth protests grow as election looms
CNN's Rafael Romo, Miguel Marquez, Krupskaia Alis, Ariel Crespo, Rey Rodriguez, Rene Hernandez and CNNMexico.com contributed to this report.
