Updated

Lawyers for Mexico's main leftist party urged the country's top electoral court to order a recount in the disputed July 2 presidential vote, while their candidate, Andres Manuel Lopez Obrador, summoned his supporters to the streets to claim he was the rightful winner.

Lopez Obrador promised a record number of protesters would flood the capital's main square on Sunday to back his allegations of electoral fraud, in the third mass demonstration called by the former Mexico City mayor since the election.

On Saturday, three of Lopez Obrador's lawyers asked the Federal Electoral Tribunal to declare Lopez Obrador president-elect, arguing that there were mathematical errors, falsifications or other problems at 72,000 of the country's 130,000 polling places.

The seven-judge panel is weighing 364 challenges to an official count that gave Felipe Calderon, of outgoing President Vicente Fox's National Action Party, a slight advantage over Lopez Obrador, who stepped down as the capital's mayor last year to run for president.

The closed-door session was the court's first hearing since the vote. Calderon's lawyers were expected to outline their case Sunday. National Action officials have submitted evidence they say shows the election was clean, while also filing their own challenges in districts that voted heavily for Lopez Obrador.

Addressing a group of National Action mayors at his party's headquarters on Saturday, Calderon promised to unify Mexico and defended the integrity of the vote.

"The election was clean, it was competitive, it was closely observed," he said. "At the end of the day, we won the presidential election. Period."

An official count the week following the election gave Calderon an advantage of less than 0.6 percent, about 240,000 votes out of 41 million cast. The Federal Electoral Tribunal has until Sept. 6 to either declare a winner or annul the election.

Lopez Obrador, a populist who counts on millions of passionate supporters who have turned out to support him in past disputes, says widespread fraud and a dirty campaign are responsible for Calderon's narrow lead. He has called for a vote-by-vote recount he says will prove he was the winner.

His attorneys told the tribunal that Calderon enjoyed his largest advantages at polling places where there were no observers from Lopez Obrador's Democratic Revolution Party, and that many of the votes annulled by electoral officials were in favor of Lopez Obrador.

Attorney Ricardo Monreal described the judges as respectful and attentive, and said the lawyers urged them to make an "exemplary ruling."

He also called Fox — who leaves office Dec. 1 — "inept," and accused his administration of using its power and money to influence the election.

"The court should not uphold the illegal intentions of the president," Monreal said, adding that the judges' decision "affects not only the rule of law in the country, but also society and democracy."

After weeks of protests and allegations that Mexico is slipping back to its fraudulent electoral past, many have begun to question the Federal Electoral Institute, the autonomous body responsible for organizing the election.

Democratic Revolution lawyer Arturo Nunez said Saturday that by ordering a ballot-by-ballot recount the judges could "clear up any doubt about the election," allowing the eventual winner to "legitimately confront the challenges of the presidency."

Demonstrators, including a masked wrestler nicknamed "Little Ray of Hope," have camped out in front of the electoral court for weeks to pressure the judges for a recount.

"Calderon is a thief who won't benefit anyone but the rich. That's why we the poor are here," said protester Julieta Martinez, a 43-year-old federal employee who said she has spent all of her free time demonstrating in front of the court.

Calderon claims a recount would violate electoral laws designed to protect against fraud. He cites legislation that says officials can reopen sealed vote containers only where there is evidence of irregularities.