More than 100,000 people have gathered in Mexico City to support demands for a recount after last weekend's hotly disputed presidential election.
The rally was called by losing candidate Andres Manuel Lopez Obrador.
He says he will go to the country's election tribunal and to court to overturn an election he alleges was "plagued with irregularities".
Felipe Calderon of the ruling National Action Party won 35.88% of the vote, against 35.31% for Mr Lopez Obrador.
Tightly-packed crowds in the capital's vast main square cheered wildly as the populist Mr Lopez Obrador appeared on the giant television screen over a stage.
Huge banners denounced Mr Calderon and accused him of electoral fraud.
Mr Lopez Obrador demanded a full recount by hand of all 41 million ballots cast in what was only the second election in this deeply divided country since the end of one-party rule.
"We are going to ask that they clean up the elections," he told his supporters, many of them from Mexico's poor and working classes.
"We are going to ask that they count all the votes, vote-by-vote, poll-by-poll."
He has said he will ask the country's Federal Electoral Tribunal and the Supreme Court to look into the allegations of fraud and vote-rigging.
Mr Lopez Obrador, the candidate of the Party of the Democratic Revolution (PRD), said ahead of the rally: "The votes were counted but were badly counted. They were counted to favour the right-wing candidate."
He said Saturday's rally would be the first of several but vowed all would be peaceful.
He added that he intended to call for a march from electoral districts all over the country to the capital if his demand for a manual recount was not carried out.
The vote will not be declared complete until the electoral tribunal certifies the count.
Parties must file complaints by Monday and the tribunal must certify the winner by 6 September. It has the power to alter results and even call new polls.
Election monitors from the European Union said on Friday they found no irregularities in last Sunday's election.
A number of international leaders, including US President George W Bush, have congratulated Mr Calderon on his victory.
However, supporters of Mr Lopez Obrador are highly sceptical of the vote result.
Some fear they are witnessing a repeat of the 1988 elections, when a substantial lead by the leftist candidate, Cuauhtemoc Cardenas, disappeared during what was described as a "computer crash" by election authorities.
The candidate of the PRI - the Institutional Revolutionary party that dominated Mexican politics from 1929 until 2000 - won by a narrow margin.
But this year's election was held under newly designed rules to eliminate the vote rigging and fraud of the past.
They allow for challenges to the result until September, and a president must be sworn-in in early December.