The leftist candidate, Andrés Manuel Lopéz Obrador, a former Mexico City mayor who champions the cause of the poor, did not immediately react to the ruling, but was to appear Saturday evening in the capital’s central square, the Zócalo, to tell his followers what his next move would be.

The judges ordered that the votes in the July 2 election be recounted in only 11,839 of the 130,000 polling places. They rejected the Mr. López Obrador’s argument that there were enough human errors and, in some instances, evidence of fraud to warrant recounting all the votes. They also noted the left-wing Party of the Democratic Revolution had failed to challenge the results in 70 electoral districts, and that under law, those results must stand.

Leonel Castillo, the chief judge of the electoral tribunal, defended the integrity of Mexico’s electoral system in general, pointing out fraud was nearly impossible because citizens chosen at random and trained to be poll workers were responsible for counting the vote on election night.

“Citizens provide the certainty of the computation process,” he said. “This is the method and the way that the law makes the elections certain.”

Other judges echoed his view, rejecting Mr. Lopéz Obrador’s contention that there was a plot among poll workers in some states to pad his opponent’s totals.

“The election method is ingenious,” Magistrate Mauro Miguel Reyes Zapata said. “It’s ingenious, and we can assume it is secure, because it is the citizens who carry it out and organize it.”

But there was apparently still a chance that a further recount could be ordered. Lorenzo Cordova, a law professor who specializes in election law, said the court could order a recount of more polling places later on if the recount this week reveals signs of fraud.

“This recount, although it’s partial, will permit one to find evidence of whether there was fraud or not,” he said. “It opens the door to the possibility of knowing if Mr. Lopéz Obrador’s accusations have merit or not.”

Last month, an official tally handed a narrow victory to Felipe Calderón, the conservative candidate from President Vicente Fox’s governing National Action Party. The count showed Mr. Calderón won by 243,000 votes. Mr. López Obrador has argued there were arithmetical errors in at least 72,000 polling places and evidence of fraud in about 600.

Over the last month, Mr. López Obrador has said repeatedly he would not accept anything less than a full recount of the 41 million votes cast and has suggested he will employ increasingly belligerent acts of civil disobedience if he does not get his way.

Outside the courthouse, about 200 protesters burst into shouts as news of the ruling spread, hurling insults at the judges and blocking the doors so no one could leave. Some carried placards that said: “Sold-out judges,” “You are a shame to Mexico” and “How much did they pay you?”

In recent days, political operatives connected to Mr. López Obrador have said there was a move afoot to bribe the panel, though they offered no proof.

Arturo Nuñez and Ricardo Monreal, two lawyers for Mr. López Obrador, stormed out of the courthouse before the vote as soon as it became apparent the judges would not grant their request.

A spokesman for Mr. Lopez Obrador, Cesar Yañez, said the candidate was closeted with his closest advisers, hammering out a plan of action. His supporters have already blockaded the main artery of the capital, Avenida Reforma, for miles, tying up traffic and hurting businesses.

The judges ruled there were arithmetic errors and other irregularities that warranted a recount of votes in about 10 percent of the polling places. Those polling places are located in 145 of the 300 electoral districts and 26 of the 32 states.

Chief Magistrate Castillo said Mr. López Obrador’s lawyers had failed to provide enough evidence of irregularities to throw the entire count into doubt.

Instead, the panel voted to order electoral judges in those states to conduct the partial recount over five days starting next Wednesday. After the recount, they will rule on whether to annul the results from those polling places or to accept the new totals. Next, the judges must certify that the election was fair and name the new president-elect by Sept. 6.

Lorenzo Cordova, a law professor who specializes in election law, said the court’s ruling could lead to a recount of more poling places later on if the recount this week reveals signs of fraud.

“This recount, although it’s partial, will permit one to find evidence of whether there was fraud or not,” he said. “It opens the door to the possibility of knowing if Mr. Lopéz Obrador’s accusations have merit or not.”