Mr Calderon’s leftist rival, Andres Manuel Lopez Obrador, dismissed the claim and questioned the result.
Acording to preliminary results posted by the the Federal Electoral Institute Mr Calderon won by a razor-thin margin but Mr Obrador is demanding a recount.
Adding to the suspense, Mexico’s Federal Electoral Institute (IFE) said it would not declare the winner of Sunday's election until it certifies the results later in the week.
Mr Calderon, of the ruling National Action Party (PAN), had just over 36 percent of the vote and a one-point lead over Mr Obrador with all but about two percent of the ballots counted.
Mr Obrador, a left leaning former mayor of Mexico City, champions the cause of the millions of impoverished Mexicans.
"Today I can assure all Mexicans I won the election," Mr Calderon, 43, told the Televisa network. "There is a result, it is irreversible."
However, Mr Obrador, 52, told the TV network he would closely scrutinise the vote counts provided by every polling station and would accept defeat only if it is clearly proven he had lost.
Obrador defiant
Mr Obrador who leads the Party of the Democratic Revolution (PRD) did not rule out calling his supporters onto the streets. "If we won, even by one vote, I will defend it," he said.
The political cliff hanger was being closely followed by Washington, which had hoped to see a reversal of the trend that brought several leftist leaders to power across Latin America in recent years.
But the US administration has insisted that it will work with whoever wins the election.
A lifelong politician, Mr Calderon has served as a parliamentarian, PAN party president, and as energy minister in the cabinet of President Vicente Fox, whose 2000 victory ended 71 years of authoritarian rule by the Institutional Revolutionary Party (PRI.)
Mr Calderon says he wants to encourage foreign investment and slash corporate taxes in order to boost economic growth and create badly-needed jobs.
But Mr Obrador claims the wealth is not trickling down to the millions who live on less than two dollars a day and who in many cases risk their lives by crossing the northern border illegally in search of the American dream.
Mexico's next president, who will take office on December 1, will face formidable challenges in trying to fulfill campaign pledges of battling poverty, corruption, common crime and drug-fueled violence.