Tight security still in evidence after the week's upheaval
While not expressing personal support for Mr Chavez - renowned for his fiery rhetoric - Latin American leaders condemned "the interruption of constitutional order in Venezuela".
Mr Chavez was forced to step down after the deaths of at least 13 anti-government protesters in violence on Thursday night.
Laws repealed
At a sombre ceremony on Friday, Mr Carmona, 60, a former oil executive, was sworn in as interim president.
He quickly moved to repeal dozens of controversial economic laws and dissolved the Supreme Court and the National Assembly.
Promising presidential elections within a year, Mr Carmona said: "We can achieve the governability required to improve Venezuela's image."
"The strongman era has ended."
Latin American leaders, at a Group of Rio meeting in Costa Rica, expressed regret at the loss of life on Thursday, but also concern at the manner of Mr Chavez's downfall.
Washington blamed Mr Chavez for creating the conditions that led to his removal.
International concern
But the US and Spain later issued a joint statement calling for calm, an end to violence and a swift return to normality with a "guarantee of fundamental rights and freedoms".
UK Foreign Office Minister Denis MacShane, who met Mr Chavez just a few days ago, said he hoped the president's resignation would prevent more bloodshed.
But elections should be held as soon possible, he said.
"Any delay to this process will be contrary to Venezuela's long history of democracy and unacceptable to the international community."
Cuba, a staunch supporter of Mr Chavez's left-wing policies, has expressed concern for his safety.
He was initially being held at the Fuerte Tiuna military base in the capital, Caracas.
But Cuban television broadcast an interview with his daughter, Maria Gabriela Chavez, who said there were reports he had been moved to an undisclosed location.
The army has rejected his plea to be allowed to go into exile in Cuba.
Army General Roman Fuemayor said: "He has to be held accountable to his country."
Chavez's version
Military leaders said Mr Chavez resigned at their insistence after he ordered troops and civilian gunmen to fire on a crowd of more than 150,000. At least 13 people died and more than 240 were injured.
But Mr Chavez's daughter insisted he was the victim of a coup.
"It is a lie, all lies. He said he never resigned, that a group of military took him away and he is being held incommunicado," she said.
Mr Chavez won a landslide victory in 1998, six years after he led an abortive coup as a young paratroop officer.
Following events of the last few days, oil production and distribution are beginning to return to normal for the world's fourth-largest oil producer after workers abandoned their action.
But PDVSA has suspended oil exports to Cuba in protest at Havana's support for Mr Chavez who agreed cheap rates with President Fidel Castro.