In a brief speech to the National Assembly, Nicolas Maduro pledged loyalty to the president and said Hugo Chavez remained in charge of the country.
Nicolas Maduro also denied that there was a political fight for the succession.
President Hugo Chavez was due to be sworn in on January 10 for a fourth term.
The Supreme Court ruled he could take the oath at a later date, a view challenged by opposition figures.
“There is only one president: Hugo Rafael Chavez Frias, supreme commander of the army, commander of the Bolivarian Revolution,” Nicolas Maduro told legislators.
Nicolas Maduro also used his speech to announce that Hugo Chavez had appointed former vice-president Elias Jaua as Venezuela’s new foreign minister.
The post was previously held by Nicolas Maduro.
The vice-president saluted National Assembly president, Diosdado Cabello, and dismissed rumors that they are political rivals.
“They say Cabello and I are fighting. But Cabello and I are united in our heart, in loyalty to a man who has the supreme command of this country.”
The vice-president said that his appearance to give the state of the union address was in accordance with the constitution, as Hugo Chavez had been granted leave of absence by the National Assembly.
This view was challenged by some legal experts – they highlight Article 237 of the Constitution, which stipulates that the president should appear “personally” to give the speech within 10 days of the inauguration of the legislature.
The current assembly was sworn in on January 5.
The speech, which in Hugo Chavez’s hands could go on for hours, lasted a matter of minutes with Nicolas Maduro.
President Hugo Chavez underwent a fourth operation for cancer on December 11, and suffered post-operative complications.
Nicolas Maduro told legislators he had met Hugo Chavez in Havana on Monday and that his health was improving.
“He is climbing the hill, he is fighting with his spirit, his vision, his love,” said Nicolas Maduro, adding that Hugo Chavez has been briefed on developments in Venezuela.
Supreme Court justices have ruled that Hugo Chavez, who has been in office since 1999, can be sworn in for another term as president at a later date.
Opposition leaders say the government is riding rough-shod over the constitution and have demanded clarity about who is running the country.
According to the constitution, if a president is permanently incapacitated, the speaker of the National Assembly should take over and elections called within 30 days.
If the absence is temporary, the vice-president assumes charge for a maximum of 180 days.
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