In a televised address from Havana, Nicolas Maduro said Hugo Chavez continued to be in a “delicate state”.
Hugo Chavez underwent his fourth cancer operation on December 11 in Cuba but suffered a respiratory infection.
The president – who has been in power since 1999 – won another term in October’s election.
Nicolas Maduro did not give details about Hugo Chavez’s condition but said the latest complications were connected to the respiratory infection.
“We have been informed of new complications that arose as a consequence of the respiratory infection we already knew about,” he said.
“The president gave us precise instructions so that, after finishing the visit, we would tell the [Venezuelan] people about his current health condition.
“The state of health of President Chavez continues to be delicate.”
He added that the treatment was “not without risk.”
Nicolas Maduro, appearing solemn, spoke alongside Hugo Chavez’s eldest daughter, Rosa, his son-in-law Jorge Arreaza, and Venezuelan Attorney General Cilia Flores.
The vice-president said he would remain in Havana “for the coming hours” but did not specify how long.
Late on Sunday, Venezuela’s Information Minister Ernesto Villegas said a government-organized New Year’s Eve concert in central Caracas had been cancelled and he urged Venezuelans to pray for President Chavez.
It is now three weeks since Hugo Chavez has been seen or heard from in person.
There continues to be huge secrecy surrounding his precise condition.
There are also many questions about what will happen on January 10 when Hugo Chavez is due to be re-inaugurated.
National Assembly head Diosdado Cabello recently said that the swearing-in ceremony would be delayed in the case of Hugo Chavez’s absence.
However, opposition leaders say postponing the inauguration would be unconstitutional.
The constitution states that if there is an “absolute absence” of the president, elections must be held within 30 days.
Hugo Chavez has said that, should his health fail, Venezuelans should vote for Nicolas Maduro in fresh elections.
Officials have never disclosed the type or severity of Hugo Chavez’s cancer, which was first diagnosed in June 2011.
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