The marchers, numbering at least 10,000, walked or rode on horseback in separate groups from around Mexico City to its central square on Wednesday and said they would not back down until electoral authorities accepted that Andres Manuel Lopez Obrador had won the vote.
The left-wing presidential candidate, who had promised to govern for the country's poor, called on his supporters from around the country to start gathering in the capital from Wednesday.
A huge march is planned for Sunday to the Zocalo, one of the world's largest municipal squares.
His party estimated that 40,000-50,000 supporters were on the move ahead of the rally.
Official results show that Felipe Calderon, the election's conservative candidate, won the election by 0.58%, but Lopez Obrador claimed widespread fraud.
An electoral court now has until the start of September to decide on the country's president.
"I won the presidential election, I am more and more sure of that"
Andres Manuel Lopez Obrador,
"I won the presidential election, I am more and more sure of that," Lopez Obrador said on Wednesday at a news conference, where he played video footage that he said showed polling stations where Calderon's votes were over counted.
Lopez Obrador believes a nationwide vote-by-vote recount is the only way to settle doubts.
"Andres Manuel won the election and they want to impose someone else - we've had enough of fraudsters," said Gloria Moran, one of the protesters at Wednesday's march.
"We won't let the other one (Calderon) take office."
Calderon has already formed a team to oversee a smooth transition of power from fellow conservative Vicente Fox, the president.
He denies fraud and says a vote-by-vote recount is not legally possible in Mexico. He urged the country to stay calm and warned his rival not to provoke violence.
Despite a string of allegations by the leftist over irregularities in the vote count, campaign overspends and pro-Calderon bias among electoral authorities, the election was ruled free and fair by European Union observers.
However, many Mexicans are sensitive to suggestions of fraud, following generations of vote rigging under the Institutional Revolutionary Party, which ruled the country for 71 years until knocked from power by Fox in 2001.
More than 100,000 people turned out in the Zocalo last weekend to back Lopez Obrador, who was the capital's popular mayor until running for president.