Venezuela has the world's second-highest murder rate after Honduras — 56 people for every 100,000 according to government figures, which nongovernmental groups say are understated.
Late Tuesday, the armed forces chief, Gen. Wilmer Barrientos, reported "complete calm" in the country.
But there had been several incidents of political violence.
In one, a group of masked, helmeted men on motorcycles, some brandishing revolvers, attacked about 40 students who had been protesting for more than a week near the Supreme Court building to demand the government give more information about Chavez's health.
The attackers, who didn't wear clothing identifying any political allegiance, burned the students' tents and scattered their food just minutes after Chavez's death was announced.
"They burned everything we had," said student leader Gaby Arellano. She said she saw four of the attackers with pistols but none fired a shot.
Outside the military hospital where Chavez's body was visited by loved ones and allies, an angry crowd attacked a Colombian TV reporter.
"They beat us with helmets, with sticks, men, women, adults," Carmen Andrea Rengifo said on RCN TV. Video images showed her bleeding above the forehead but she was not seriously injured.
Maduro and other government officials have recently railed against international media for allegedly reporting rumors about Chavez's health, although RCN wasn't one of those criticized.
After nightfall, several hundred people gathered at Bolivar Square, a symbolic place for Chavistas because it has a huge nine-meter-tall (30-foot-tall) statue of Simon Bolivar, the 19th century independence hero whom Chavez claimed as his chief inspiration.
Some arrived singing Venezuela's national anthem and holding up posters of Chavez.
One man began shouting through a megaphone a warning to the opposition: "They won't return." The crowd then joined in, chanting: "They won't return."
Chavez leaves behind a political movement firmly in control of a nation that human rights activist Liliana Ortega, director of the non-governmental group COFAVIC, describes as a badly deteriorated state where institutions such as the police, courts and prosecutor's offices have been converted into tools of political persecution and where most media are firmly controlled by the government.
Maduro, whose government role had grown after Chavez went to Cuba for treatment, was belligerent early Tuesday. He reported the expulsion of one of the two U.S. attaches, and also said that "we have no doubt" that Chavez's cancer, first diagnosed in June 2011, was induced by "the historical enemies of our homeland."
Maduro compared the situation to the death of the Palestinian leader Yasser Arafat, claiming Arafat was "inoculated with an illness" and said a "scientific commission will prove that Comandante Chavez was attacked with this illness."
Chavez's inner circle has long claimed the United States was behind a failed 2002 attempt to overthrow him, and he has frequently played the anti-American card to stir up support. Venezuela has been without a U.S. ambassador since July 2010 and expelled another U.S. military officer in 2006.
U.S. State Department spokesman Patrick Ventrell rejected the assertion that the U.S. was trying to destabilize Venezuela. The claim, he said, "leads us to conclude that, unfortunately, the current Venezuelan government is not interested in an improved relationship."
Ventrell added that the assertion that Washington somehow had a hand in Chavez's illness was "absurd."
He hinted the U.S. could reciprocate with expulsions of Venezuelan diplomats.
Chavez rose to fame by launching a failed 1992 coup, but never groomed a successor and many Venezuelans find Maduro, a former union agitator and Chavez's intellectual inferior by bounds, lacking the political heft.