Defiance in the streets
But Lopez Obrador's supporters remained unconvinced.
"We are ready to do whatever is necessary," said Belasario Cruz, 32, a farmer from Tabasco. "We are tired of the rich having everything and the poor having nothing."
There were smaller demonstrations planned in cities including Tijuana on the U.S. border and San Cristobal de las Casas in the south.
Lopez Obrador, a former Mexico City mayor, has asked protesters to be peaceful and law-abiding, but also said the government would be responsible for any flare-up of anger because officials had rejected his demand for a manual recount.
There were no immediate reports of arrests or violence.
But the U.S. Embassy in Mexico City urged U.S. citizens "to avoid downtown Mexico City and surrounding areas" during the protest, noting that "even demonstrations intended to be peaceful can turn confrontational and escalate into violence."
In a meeting with foreign correspondents, Lopez Obrador said there were more irregularities in the balloting than under the Institutional Revolutionary Party, or PRI, which ruled Mexico until it was ousted by President Vicente Fox in 2000.
Calderon belongs to Fox's conservative National Action Party
"The National Action Party learned from the fraudulent practices of the PRI and it exceeded them," Lopez Obrador said.
A devoted following
Lopez Obrador's millions of extremely devoted followers religiously follow his message of helping the poor and downtrodden.
He has in the past headed protests that turned disruptive or violent.
In 1996, he led farmers and fishermen in sometimes-violent takeovers of state-owned oil wells to demand compensation for damages from an oil spill.
Last year, as Mexico City mayor, he led huge street protests that forced Fox to fire his attorney general and drop a legal case that would have kept Lopez Obrador out of the presidential race.
These days, Lopez Obrador must walk a tightrope. If he appears too radical, he risks hurting his party and its chances in the next presidential elections in 2012. If he appears too moderate, he risks disappointing his core supporters.
"His political stock would increase greatly for 2012" if he finds a way to concede defeat gracefully, political analyst Oscar Aguilar said.
Lopez Obrador says he will challenge the result in electoral tribunals and in the Supreme Court. He claims hundreds of thousands of votes for him remain uncounted, miscounted or voided.
Electoral authorities say the law allows such a recount only where credible evidence of irregularities exist for a specific polling place.
Aguilar predicted that Lopez Obrador would never recognize Calderon's narrow electoral victory.
"He will never concede defeat," Aguilar said. "Once the election results are certified, he will open a permanent campaign of criticizing the government."