Opposition coalition leader Ramon Guillermo Aveledo said at a news conference that the information provided by government officials "continues to be insufficient."
Chavez has not been seen or heard from since the December 11 operation, and Vice President Nicolas Maduro on Tuesday said the president's condition remained "delicate" due to complications arising from a respiratory infection.
Maduro also urged Venezuelans to ignore rumors about Chavez's condition. Aveledo said the opposition has been respectful during Chavez's illness but that "the secrecy is the source of the rumors."
"They should tell the truth," Aveledo said, noting that Maduro had pledged to provide full reports about Chavez's condition. He reiterated the opposition's call for the government to release a medical report, and said all indications are that Chavez won't be able to be sworn in to begin a new term on January 10.
If Chavez can't take office on that date, Aveledo said the constitution is clear that the National Assembly president should then take over temporarily until a new election is held. He said what happens next in Venezuela should be guided by "the truth and the constitution."
If Chavez dies or is unable to continue in office, the Venezuelan Constitution says a new election should be held within 30 days.
With rumors swirling that Chavez had taken a turn for the worse, Maduro said on Tuesday that he had met with the president twice, had spoken with him and would return to Caracas on Wednesday.
"He's totally conscious of the complexity of his post-operative state and he expressly asked us ... to keep the nation informed always, always with the truth, as hard as it may be in certain circumstances," Maduro said in the prerecorded interview in Havana, which was broadcast Tuesday night by the Caracas-based television network Telesur.
Both supporters and opponents of Chavez have been on edge in the past week amid shifting signals from the government about the president's health. Officials have reported a series of ups and downs in his recovery - the most recent, on Sunday, announcing that he faced the new complications from a respiratory infection.
Maduro did not provide any new details about Chavez's complications during Tuesday's interview. But he joined other Chavez allies in urging Venezuelans to ignore gossip, saying rumors were being spread due to "the hatred of the enemies of Venezuela."
He didn't refer to any rumors in particular, though one circulating online had described Chavez as being in a coma.
Maduro said Chavez faces "a complex and delicate situation." But Maduro also said that when he talked with the president and looked at his face, he seemed to have "the same strength as always."
"All the time we've been hoping for his positive evolution. Sometimes he has had light improvements, sometimes stationary situations," he said.
Maduro's remarks about the president came at the end of an interview in which he praised Venezuelan government programs at length, recalled the history of the Cuban revolution and touched on what he called the long-term strength of Chavez's socialist Bolivarian Revolution movement.
He mentioned that former Cuban President Fidel Castro had visited the hospital where Chavez was treated, and praised Cuba's government effusively. "Today we're together on a single path," Maduro said.
Before his operation, Chavez acknowledged he faced risks and designated Maduro as his successor, telling supporters they should vote for the vice president if a new presidential election was necessary.
Maduro didn't discuss the upcoming inauguration plans, saying only that he is hopeful Chavez will improve.
The vice president said that Chavez "has faced an illness with courage and dignity, and he's there fighting, fighting."
"Someone asked me yesterday by text message: How is the president? And I said, 'With giant strength,'" Maduro said. He recalled taking Chavez by the hand: "He squeezed me with gigantic strength as we talked."