"Those who die for life cannot be called dead," Maduro said, surrounded by military officials and key Cabinet members.
Maduro also called on the opposition to show respect during this time of national mourning.
"Let there be no violence, let there be no hate," he said. "The only sentiment that Chavez had was love, love for life, for the country and for the future."
Defense Minister Diego Molera said troops would be on the streets to guarantee order and he said Maduro and the Cabinet have the military's full backing.
At Plaza Bolivar, an iconic square in the heart of Caracas, mourners chanted "Chavez lives! The struggle continues!" They also clutched pictures of their hero.
Reaction to the death poured in from around the world. President Barack Obama said the U.S. stands by the Venezuelan people "at this challenging time" and is interested in "developing a constructive relationship" with the South American country.
The president's comments came despite Venezuela's expulsion earlier Tuesday of two military attaches assigned to the U.S. Embassy in Caracas. Maduro accused the men of spying and gave them 24 hours to leave the country. The Pentagon denied the accusation.
Canadian Prime Minister Stephen Harper issued a similar statement to Obama's, offering his condolences to the people of Venezuela.
"At this key juncture, I hope the people of Venezuela can now build for themselves a better, brighter future based on the principles of freedom, democracy, the rule of law and respect for human rights," Harper said.
Bolivan President Evo Morales, a longtime ally, said Chavez's death is a great loss for the region.
"We're hurt. We're shattered by the passing of our brother and companion," Morales said. "My companion gave his entire life for the liberation of Venezuela, Latin America, and anti-imperialists and anti-capitalists of the world."
In Haiti, which is heavily dependent on oil and other aid from Venezuela, President Michel Martelly tweeted "sincere condolences." Haitian Prime Minister Laurent Lamothe told The Miami Herald: "Today is a sad day. The world has lost a great leader in President Hugo Chavez. Haiti will forever be grateful to him."
U.S. Rep. Ileana Ros-Lehtinen, R-Fla., said Chávez's death presents an opportunity for Venezuelans to "emerge from this oppressive regime and regain their democracy and human rights."
"Chavez misruled Venezuela with an iron grip on the government, economy and the courts as he routinely bullied the media and the opposition to deny the people of Venezuela their basic freedoms," said Ros-Lehtinen, former chairwoman of the House Foreign Affairs Committee. "Today his death marks the end of this tyrannical rule but the road to democracy for the Venezuelan people is still very much uncertain."
Chavez was in power for 14 years and his death should spark new elections within 30 days. Maduro, a one-time union organizer and longtime foreign minister, is expected to hold an edge over potential rivals, including Miranda Gov. Henrique Capriles.
Chavez had not been seen in public or heard from in almost three months, after he underwent a fourth round of surgery in Cuba to treat an undisclosed form of cancer.
Maduro said funeral arrangements would be announced later Tuesday, but called the nation together at an iconic park and in front of the hospital where Chavez had spent the last two weeks. Minister: Maduro is interim leader
Caracas, Venezuela • Venezuela's foreign minister said Tuesday that Vice President Nicolas Maduro will be interim president in the wake of Hugo Chavez's death and run as the governing party candidate in elections to be called within 30 days.
Four hours after Chavez's death was announced, Foreign Minister Elias Jaua told the Telesur network that the president had clearly stated in December what should occur if he died.
Chavez said Maduro should be the Socialist Party candidate and suggested he should oversee the convening of new elections.
Venezuela's constitution specifies that the speaker of the National Assembly, currently Diosdado Cabello, should assume the interim presidency if a president can't be sworn in.
The Associated Press