* Latest health update says lung infection controlled
* Powerful government trio meet Castro, check on Chavez
* Venezuelan leader still unseen since Dec. 11 operation
* Opposition demand "truth" on president's condition
By Andrew Cawthorne
CARACAS, Jan 13 (Reuters) - Cancer-stricken Venezuelan President Hugo Chavez's lung infection has been controlled and his medical state is improving more than a month after his latest surgery in Cuba, the government said on Sunday.
"Despite his delicate state ... in recent days the general medical evolution has been favorable," said the latest official health update, which was relatively positive compared to others but still illustrated the gravity of Chavez's situation.
"The respiratory infection is controlled, though the commander-president still requires specific measures to solve breathing insufficiency ... he is conscious."
The communique, which gave no more details on his condition, came as the three most powerful government figures after Chavez gathered in Havana to check on him and meet with Cuban allies.
Vice-President Nicolas Maduro, Congress head Diosdado Cabello, and Oil Minister Rafael Ramirez have been shuttling to and from Cuba since the 58-year-old socialist president's fourth and most serious cancer operation a month ago.
Chavez, who missed his own inauguration for a new, six-year term last week, has not been seen or heard from in public since the surgery. Many Venezuelans are assuming his momentous 14-year rule of the South American OPEC nation could be nearing an end.
"We are all Chavez!" and "Chavez will return!" were among slogans sang and chanted at numerous solidarity rallies, meetings and concerts across Venezuela over the weekend, which drew thousands of passionate and anxious supporters.
Venezuelan state TV on Sunday even split its screen into four to show events going on around the nation.
"The situation is complex and delicate," Elias Jaua, a former vice-president and ally of Chavez, told one rally.
"He continues battling for his life."
Villegas said Maduro, whom Chavez has designated his successor, informed his boss of the outpouring at home.
State media said Maduro, Cabello, Ramirez - who also heads the powerful state oil company PDVSA - and Attorney General Cilia Flores all met Cuban President Raul Castro over the weekend. But there were no details of the talks.
The joint presence of top Venezuelan officials in Havana inevitably deepens rumors that Chavez is at death's door - and draws opposition criticism that Raul and Fidel Castro are giving instructions behind the scenes.
"We know which commander is giving the orders to Chavista leaders," opposition legislator Maria Corina Machado tweeted sarcastically, in a reference to the Cuban president.
Officials have been lashing "necrophilic" opponents for such criticism, and Chavez's brother said on Saturday that he was improving daily and not in a coma as rumored.
Another opposition leader, Julio Borges, said the secrecy around Chavez's precise condition was unacceptable.
"No one is asking for details of the operation or the president's treatment, but that simply they tell the truth about his health prognosis," said Borges, a right-wing legislator who wants Chavez formally declared absent from office.
That would trigger the naming of a caretaker president, and an election within a month. But Venezuela's Supreme Court has ratified that Chavez remains president with Maduro in charge as No. 2 until Chavez's health situation is clarified.
"It's been a year-and-a-half of contradictions and announcements of his complete curing followed by relapses," Borges added, saying problems like inflation, housing shortages and power-cuts were being neglected during a political impasse.
Since the disease was discovered in mid-2011, Chavez has wrongly declared himself cured twice, in an extraordinary and unsettling saga for Venezuela's 29 million people.
The stakes are high for the wider region too. Cuba and a handful of other leftist-ruled nations have for years been depending on Chavez's aid to bolster fragile economies.
Should Chavez die or be incapacitated, the most likely next step would be an election pitting Maduro, 50, against Henrique Capriles, 40, the main opposition leader who lost to Chavez in an October presidential election.
In an opinion column on Sunday, Capriles railed against the "national paralysis" but said the opposition would not be drawn into confrontation or street protests. That tactic failed spectacularly for them a decade ago when Chavez was briefly toppled but came back stronger than before.
"Just as the president has the right to attend his ill health, so Venezuelans do not deserve urgent problems to be put on hold," Capriles said. "We are not going to play the game of calling people onto the street to create a confrontation that will benefit the violent and radical ones."