* Election official says Pena Nieto has "irreversible" lead
* PRI stages comeback after losing power in 2000
* Leftist candidate refuses to concede defeat
By Anahi Rama and Lizbeth Diaz
MEXICO CITY, July 1 (Reuters) - The party that ruled Mexico for most of the 20th century claimed victory in a presidential election on Sunday as a senior election official said the party's candidate, Enrique Pena Nieto, held an irreversible lead over his rivals.
The telegenic candidate of the Institutional Revolutionary Party (PRI) had about 38 percent support and a lead of least 6 percentage points over his nearest rival, according to an official "quick count" by election authorities.
A series of exit polls also gave Pena Nieto a clear victory.
The election completed a dramatic comeback for the PRI, which ran Mexico as a virtual one-party state for 71 years before it was finally ousted in a 2000 election.
"Mexicans have given our party another chance. We are going to honor it with results," Pena Nieto told supporters in the capital shortly after the quick count was announced.
"The result is irreversible," Benito Nacif, one of the Federal Electoral Institute's board members, told Reuters.
Departing President Felipe Calderon of the conservative National Action Party, or PAN, congratulated Pena Nieto on his victory, but the second-placed leftist challenger Andres Manuel Lopez Obrador refused to concede defeat.
"The last word has not yet been spoken," he told supporters.
Lopez Obrador could choose to challenge the election, as he did six years ago when he narrowly lost to Calderon and launched months of protests against alleged fraud.
He has said in recent weeks that this election campaign was plagued with irregularities, raising concerns that he might again call his supporters onto the streets.
Josefina Vazquez Mota of the PAN trailed in third place in Sunday's election with no more than 26 percent of the vote, the official quick count said.
Her campaign suffered from the often barbaric violence in Mexico's drug war, which has claimed some 55,000 lives since Calderon deployed the army against trafficking cartels early in his presidency.
Pena Nieto persuaded many Mexicans his government would do a better job of reducing the violence.
"The fight against crime will continue, yes, with a new strategy to reduce violence and above all protect the lives of all Mexicans," Pena Nieto said in his victory speech.
He also dismissed critics' suggestions that the PRI might try to reach a deal with one or more drug cartels in an effort to eliminate more troublesome rivals. "Let it be very clear: There will be no deal, no truce with organized crime."
An effective campaigner, Pena Nieto has also promised to boost economic growth, open state-owned oil monopoly Pemex to foreign investors, raise tax revenue and liberalize the labor market.