(Releads, updates and adds comments from candidates, Calderon and federal election agency)
Mexicans are voting Sunday in general elections that have been marked by delays in the opening of some polling places and a few isolated incidents.
The presidential election is expected to return the Institutional Revolutionary Party, or PRI, which governed Mexico from 1929 to 2000, to power.
The polls opened at 8:00 a.m. and will remain open for 10 hours.
Enrique Peña Nieto, the PRI candidate, was the frontrunner in all the polls going into the election.
Peña Nieto voted in Atlacomulco, a city in Mexico state, which surrounds the Federal District and forms part of the Mexico City metropolitan area.
"The winner will be the people of Mexico," who are "enjoying a festival of democracy," Peña Nieto, who governed Mexico state from 2005 to 2011, told reporters.
The PRI lost the 2000 and 2006 presidential elections to the conservative National Action Party, or PAN.
Andres Manuel Lopez Obrador, candidate of the leftist Progressive Movement coalition and the No. 2 candidate in the polls, narrowly lost the election six years ago to the PAN's Felipe Calderon.
Lopez Obrador, a former Mexico City mayor, lost the 2006 presidential election to Calderon by 0.56 percent and has never recognized the results.
The leftist candidate, who voted at a polling place in Mexico City, told reporters he felt "pretty good" and planned to organize "a national civic celebration" on Sunday night.
Lopez Obrador waited in line to vote because his polling place opened late, finally casting his ballot just after 9:00 a.m.
PAN presidential candidate Josefina Vazquez Mota, who was running third in the polls, voted in Huixquilucan, a city in Mexico state, surrounded by her family.
"All citizens should go out and vote without fear, with their families," Vazquez Mota said before voting.
The PAN candidate, who was accompanied by her husband, Sergio Ocampo, and three daughters, Maria Jose, Montserrat and Celia, told reporters she was "calm and happy."
The fourth candidate in the race is Gabriel Quadri, of the New Alliance Party, or PANAL, a longshot who has been drawing about 2 percent support in the polls.
Quadri voted at a polling place in the southern section of Mexico City and said he planned to watch the final of the 2012 European Championship between Spain and Italy later in the day.
"I hope that everyone will accept (the results of the election) immediately," Quadri said.
President Calderon, for his part, said the election was taking place normally but there had been some unspecified incidents.
"There have been some incidents, some of a certain amount of concern," but "the authorities are dealing with them," Calderon, who leaves office on Dec. 1, said.
"Mexico being able to vote in freedom is a privilege," Calderon said.
Sunday's election will be the largest in Mexico's history in terms of both number of eligible voters and total public offices up for grabs.
Some 80 million people are eligible to vote in the general elections, with the presidency, 628 congressional seats and thousands of other posts on the line.
A total of 141,153 polling places will be open across the country, and the voter participation rate, according to public opinion surveys, is expected to be around 60 percent.
Nearly 1 million people trained by the Federal Electoral Institute, or IFE, will handle the voting process, which is being monitored by 2 million party representatives, more than 30,000 Mexican election observers and 696 foreign election observers.
The candidates should "honor the will of Mexicans and respect the verdict of the polls," the IFE said.
"The IFE repeats once again that it is acting impartially and guarantees that every vote will be counted and can be cast with freedom," IFE chairman Leonardo Valdes Zurita said.
This will be "the biggest election day in our history and also the most watched," Valdez Zurita said.
The 45-year-old Peña Nieto had a lead of more than 10 percentage points over Lopez Obrador in the last polls released ahead of the election.
The photogenic Peña Nieto has been portrayed in the media as the new face of the PRI.
The parties used the last hours before the election to trade allegations about dirty tricks and irregularities in the financing of the campaigns.
Experts say it is nearly impossible for massive fraud to occur at the polls, but they acknowledge there is still the potential for irregularities in Mexico, which has a long history of rigged elections.
The presidential campaign was marked by the emergence of a national student movement that called for a clean election, change and an end to manipulation of the political system by Mexico's huge media companies.
The student movement, known as "Yo soy 132," staged a march Saturday that drew thousands of people to the Zocalo, Mexico City's largest plaza.
The protest movement started on May 11, when Peña Nieto visited the Universidad Iberoamericana and was jeered by students, who accused him of being a candidate "manufactured" by the powerful Televisa network.
Those in Peña Nieto's inner circle and some media pundits downplayed the incident, accusing the students of being agitators.
The students counterattacked by making a video that was posted on YouTube.
The criticism led to the birth of the "Somos mas de 131" (We Are More Than 131) movement, which took its name from the number of students who appeared in the video and later evolved into the "Yo soy 132" (I Am 132) movement when students from other universities joined the protests.
The movement's main demand is for impartiality in media coverage of political campaigns, but it has also come out against the candidate of the PRI.
Figures from the Preliminary Election Results Program, or PREP, will be released starting a few hours after the polls close for Sunday's general elections, the IFE said.
PREP figures are informative in nature and not considered final results, and they are not legally valid or a substitute for the tallies from Mexico's 300 election districts, which will begin their counts on July 4, the IFE said. EFE