Pena Nieto said "We all won in this election. Mexico won."
Mexican opposition candidate Enrique Pena Nieto's campaign team has claimed victory in the country's presidential election after exit polls showed him winning by a comfortable margin.
Pena Nieto, 45, of the Institutional Revolutionary Party (PRI), led by between eight and 11 percentage points in exit polls published by three of Mexico's main television networks after voting ended on Sunday night.
In a nationally televised speech, Pena Nieto told supporters: "I assume, with great commitment, in full responsibility, the mandate that Mexicans have given me today ... Today, July 1st, it's been the citizens who spoke and they did it with absolute clarity when they voted for a change with direction."
The opposition Institutional Revolutionary Party (PRI) was shown to have between 37.9 and 38.55 % of the vote, ahead of second-placed leftist challenger Andres Manuel Lopez Obrador, from the Party of the Democratic Revolution (PRD), who had between 30.9 and 31.86% of the vote.
Thousands of police were on duty for the vote, amid fears of intimidation from drug gangs.
Mexicans were also electing a new congress and some state governors.
Celebrations at the headquarters of the PRI started after the polls closed. Pena Nieto declared: "We all won in this election. Mexico won."
"This is just the start of the work we have before us."
He thanked Mexican voters for giving the PRI a second chance, saying his administration would have a "new way of governing".
The election campaign was dominated by the economy and the war on drugs.
"There will be no pact nor truce with organised crime,"Pena Nieto said.
He had been presented as the new face of the PRI, a break with the party's long and at times murky past that included links with drug gangs.
The party held on to power for 71 years until it was defeated in 2000.
By the time it lost to the PAN in 2000, the PRI had a reputation for widespread corruption, electoral fraud and
The PRI was in disarray by 2006, when its presidential candidate came in a distant third, but it has rebounded since
then and Pena Nieto gave it a new face.
He is promising to restore security to cities and towns ravaged by the drug war and also plans to reform Pemex, a proposal once considered political suicide.
Mexicans are fiercely protective of Pemex, but the PRI, which nationalized oil production in 1938, could be the one party able to liberalize the energy industry.
The PRI laid the foundations of the modern state with a nimble blend of politics and patronage that allowed it to appeal to labour unions and captains of industry at the same time.
Mexicans eventually tired of heavy-handedness that stifled dissent, rewarded loyalists and allowed widespread corruption.