National Assembly President Diosdado Cabello read a statement from Nicolas Maduro in which the vice president said Chavez's doctors say he needs more time to recuperate from his cancer surgery, El Universal reported.
Maduro said Chavez's medical condition constitutes an "irrefutable" supervening reason for postponing the inauguration under Article 231 of the Constitution, the newspaper said.
The Catholic Church of Venezuela said Monday, however, it would be "morally unacceptable" for the government to alter the Constitution because of Chavez's health.
"At stake are the good of the country and the defense of ethics. To alter the Constitution to attain a political objective is morally unacceptable," the Venezuelan Bishops Conference said in a statement read by the group's president, Bishop Diego Padron.
The Constitution is clear the current presidential term is to end and a new one is to begin Thursday, the bishops contend.
The bishops added Chavez's extended illness put "at grave risk the political and social stability of the nation."
The stability is made worse, the bishops said, because "the government has not told the people the whole truth [about Chavez's condition], which they have the full right to receive with certitude; it has only communicated, with evident difficulty, its political truth."
The bishops' statement was seen by those in the opposition as supporting their arguments that if Chavez -- who won election to a fourth term Oct. 7 but has been battling a "severe" respiratory infection since his early-December operation -- cannot be sworn in Thursday, then Cabello should become interim president.
But Cabello countered Monday "nowhere" does the Constitution state the assembly leader must become president if the president-elect cannot be sworn in Jan. 10.
"The only way is to have 'absolute absence,'" he said, citing the constitutional term for a permanent absence. And so far, he said, there is neither temporary nor absolute absence of the head of state.
"We will do what the people said [in the election] Oct. 7 -- [have] Chavez president of the republic," Cabello said.
Maduro, whom Chavez named as his desired successor before flying to Havana, has argued the presidential swearing-in is a "formality" that can be delayed indefinitely.
And he said the opposition interprets the constitution incorrectly.
Cabello, in a news conference with Maduro, said leaders from "friendly" nations would travel to Venezuela Thursday in a show of support.
"Friendly presidents, heads of government and prime ministers are coming to Venezuela to show their solidarity with Commander Hugo Chavez, with the people and with the constitution," Cabello said.
He did not say who the leaders would be.
Cabello called on Chavez supporters to participate in a mass rally in front of the presidential palace Thursday to respond to the opposition's "destabilizing" criticism.
Opposition groups plan a "civic strike" in their own show of strength.
Cabello also said the Simon Bolivar Symphony Orchestra, the apex of the nation's system of youth orchestras, would give a performance Thursday in honor of Chavez at the Teresa Carreno Cultural Complex, Venezuela's most important theater.
Marco Aurelio Garcia, a Brazilian presidential adviser who visited Cuba last week to learn about Chavez's health, told reporters in Brasilia Monday he learned in Havana the Venezuelan Constitution lets up to 180 days go by before an absolute absence must be declared, state-run Agencia Brasil reported.