The tally gave Felipe Calderon, the business-friendly conservative candidate for the ruling National Action Party (NAP), a slim victory over Andres Manuel Lopez Obrador, from the left-leaning Party of the Democratic Revolution (PRD).
The verification process begun on Wednesday should last several days, but claims of widespread irregularities could complicate and delay the procedure.
Meanwhile Lopez Obrador, the standard-bearer of the Party of the Democratic Revolution (PRD), reiterated his demand for a full manual recount of the 42 million votes cast on Sunday.
"The stability of the country is at stake," he said.
Calderon maintained that victory was his. "We can guarantee we have won the election," he said.
If he does not have his demands met, Lopez Obrador could urge millions of his supporters onto the streets to protest. But Calderon hinted that he could do the same.
"We could also call for protests, but the vote can't be replaced by demonstrations," he said.
Supporters of Lopez Obrador say
their man has been robbed
He criticised Lopez Obrador's allegations that the vote was tainted, saying: "They are trying to undermine an election without having the results to back it up."
Figures announced on Tuesday narrowed Calderon's advantage to just more than 257,500 votes, from an initial 402,700, leaving him with a lead of only 0.6 points.
The Federal Electoral Office (IFE) said the new figures took into account 2.58 million ballots that had been set aside because they appeared to contain inconsistencies.
IFE and political party officials on Wednesday started double-checking the vote counts sent in from the 138,500 polling stations to the 300 district-level offices.
Early in the day, PRD representatives demanded in several cases that specific tallies be compared with the actual ballots.
"I believe we won't know for quite some time who will be the president"
Ana Maria Salazar, legal expert
Once the verification process is completed, the parties have four days to raise legal objections, which will be considered by the Federal Electoral Tribunal, the ultimate authority in electoral disputes.
The IFE has until Sunday to announce a president-elect but the final outcome might only be decided by the tribunal, which must render its verdict on September 6.
"I believe we won't know for quite some time who will be the president," said Ana Maria Salazar, a legal expert.