A former mayor of Mexico City, Mr Obrador rejected a preliminary tally that gave a one-point lead to conservative Felipe Calderon.
Mr Obrador claims that three million votes were unaccounted for and complained about what he said were widespread irregularities.
"What's going on? That's what we want to know," asked Mr Obrador, who leads the Party of the Democratic Revolution (PRD). He called calling for a recount "polling station by polling station."
"We have lawyers ... ready to use every legal recourse," his spokesman, Cesar Yanez, said.
Mr Calderon, of the ruling National Action Party (PAN,) insisted there was no question he had an "irreversible" lead over Lopez Obrador.
His party dismissed Mr Obrador's claim that three million votes were missing, saying they had simply been set aside in the normal process of double-checking questionable results from some polling stations.
But the statements raised fears of bitter and lengthy legal disputes similar to the electoral debacle in Florida that delayed the outcome of the 2000 US presidential election by five weeks.
"The biggest similarity is we are facing the situation of a ballot by ballot recount," said legal expert Ana Maria Salazar.
"I believe we won't know for quite some time who will be the president," Ms Salazar said.
The Federal Electoral Institute (IFE) will begin to verify the tallies sent in from polling stations nationwide.
Political party representatives may raise objections to specific tallies and request they be compared with the actual ballots.
The IFE is scheduled to announce a president-elect on Sunday before it hands over to the Federal Electoral Tribunal, which will consider any formal complaints.
The tribunal, the ultimate arbiter for electoral disputes, has until September 6th to announce its verdict.
The political cliffhanger 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 insisted it would work with whoever wins the election.