The massive crowd thronged acting President Nicolas Maduro and blocked opposition candidate Henrique Capriles from registering for the April 14 vote by the 2 p.m. deadline.
Maduro also announced a change in Chavez's final resting place Monday, and the information ministry later said that officials had not decided what will happen to the late president's body.
Last week, Maduro had said the body would be embalmed and perpetually displayed in the country's military museum.
Thousands applauded from a plaza outside the National Election Commission, waving banners and holding up posters of Chavez as Maduro registered.
Many wore the red shirts and baseball caps of Chavez's ruling Socialist Party, letting out a loud cheer when acting President Nicolas Maduro arrived to sign his election papers.
Some cried as Maduro saluted them from the building's balcony, eulogizing Chavez once again as Venezuela's "father redeemer" and asking God to give him "the wisdom to allow me to carry out the orders he gave us."
Later, he launched into a speech of more than two hours in the plaza outside the building, introducing his longtime partner, Attorney General Cilia Flores, and their children and grandchildren to the crowd.
"I am not Chavez, but I am his son, and all of us together, the people, we are Chavez," he said.
Opposition supporters denounced the carefully stage-managed event as an affront to basic electoral fairness. The electoral commission is meant to play an impartial role ensuring the vote is fair and free.
Campaigning doesn't officially start until April 2, but already the two sides are at each other's throats.
Capriles announced his candidacy Sunday, while blasting Chavez's top lieutenants for trying to use the president's death to stoke passions and tilt the election.
"You are playing politics with the president's body," he said, adding that he wasn't convinced the government had been honest about when Chavez died, and had lied to the people during his long illness by insisting he would get better. The government says Chavez succumbed to cancer on Tuesday after a nearly two-year battle. It has offered almost no clinical information.
Capriles previously called Maduro a shameless liar and referred to him condescendingly as "boy."
Maduro appeared right after Capriles on state TV on Sunday, accusing "the losing, miserable candidate" of defaming Chavez and his family. He called Capriles a "fascist" who was trying to provoke violence by insulting the "crystalline, pure image of Commander Chavez."
During his speech, Maduro said Chavez's body would remain until Thursday at the military academy where it has lain in state. On Friday, it will be moved to the military museum Chavez employed as his headquarters during the failed 1992 coup, Maduro said.
He said the National Assembly would approve a constitutional amendment later this week to allow Chavez to be moved permanently to the National Pantheon, where the remains of early 19th century liberator Simon Bolivar are held.
By law, such a change to the constitution would have to be approved by voters.
Asked if the government still plans to permanently preserve and display Chavez's body, the Information Ministry said officials had not yet decided.
Analysts have voiced increasing concern about the angry rhetoric in a country that has become deeply divided during Chavez's 14 years in office, though most Caracas residents say such exchanges have been common.
Meanwhile, the administration of President Barack Obama on Monday expelled two Venezuelan diplomats in retaliation for Venezuela's expulsion of two American military attaches after Chavez died last week. U.S. officials say junior diplomats Orlando Jose Montanez Olivares and Victor Camacaro Mata were told to return home over the weekend and left the U.S. on Sunday.
Officials spoke on condition of anonymity because they weren't authorized to speak publicly on the matter.
Washington wants to repair ties with Venezuela but has made little headway so far.
Beyond the diplomatic tit for tat, Venezuelan officials have accused the U.S. of being responsible for Chavez's cancer and sought to rally anti-U.S. sentiment ahead of an April election for a new leader.
And in Cuba, revolutionary icon Fidel Castro broke his silence over the death of his protege and uber-ally, saying in an editorial published by Communist Party newspaper Granma that the island had lost its "best friend."
Cuba receives billions of dollars in oil a year from Venezuela at cut-rate prices, a huge boost its flagging economy.
Associated press writers E. Eduardo Castillo in Caracas and Bradley Klapper in Washington contributed to this report.