UPDATE 1-Venezuela furious at Obama's comments on ailing Chavez
* Sensitive moment in Venezuela over Chavez's cancer
* Socialist leader fighting to recover from operation
* Leader of Latin America's left seen as heir to Castro
CARACAS, Dec 14 (Reuters) - Venezuela's government reacted with fury on Friday to U.S. President Barack Obama's criticism of ailing Hugo Chavez's "authoritarian" government at a time of national anxiety over his battle to recover from cancer surgery.
In an interview with U.S. network Univision, Obama declined to speculate on the 58-year-old socialist president's health in Cuba, where he is in a delicate state after his fourth operation since mid-2011 for cancer in the pelvic region.
But he did say U.S. policy was aimed at ensuring "freedom" in Venezuela. "The most important thing is to remember that the future of Venezuela should be in the hands of the Venezuelan people. We've seen from Chavez in the past authoritarian policies, suppression of dissent," Obama told Univision.
Those remarks were a red cloth to officials in Caracas where emotions are running high over the future of Chavez and his self-styled revolution in the South American OPEC nation.
In power since 1999, Chavez is due to start a new six-year term on Jan. 10 after winning re-election just weeks before Obama did. His health crisis has thrown that into doubt, and Chavez has named a successor in case he is incapacitated.
"With these despicable comments at such a delicate moment for Venezuela, the U.S. president is responsible for a major deterioration in bilateral relations, proving the continuity of his policy of aggression and disrespect towards our country," the Venezuelan government said in a statement.
During his tumultuous 14-year rule, Chavez has taken former Cuban leader Fidel Castro's mantle as the U.S. government's main irritant in the region - though oil has continued to flow freely north to the benefit of both nations' economies.
Adored by poor supporters for his charismatic style and channeling of Venezuela's oil resources into a wide array of welfare projects, Chavez is regarded as a dictator by opponents who point to his often harsh treatment of political foes.
Officials said doctors had to use "corrective measures" to stop unexpected bleeding caused during Tuesday's six-hour surgery on Chavez, but his condition had since improved.
A medical update was due later on Friday.
Chavez's situation is being closely tracked around the region, especially among fellow leftist-run nations from Cuba to Bolivia who depend on his generous oil subsidies and other aid for their fragile economies.
"The president is battling hard - this time for his life, before it was for the Latin American fatherland," said President Evo Morales of Bolivia, a Chavez friend and ally who announced he was flying to Havana overnight for an "emergency" visit.
"This is very painful for us."
Chavez has not divulged details of the cancer that was first diagnosed in June 2011, sparking endless speculation among Venezuela's 29 million people and criticism from opposition leaders for lack of transparency.
"They're hiding something, I think," said Venezuelan housewife Alicia Marquina, 57. "I'm not convinced by the announcements they're making. I'm not a 'chavista', but neither am I cruel, I hope he does not suffer much and finds peace."
If Chavez has to leave office, new elections must be held within 30 days. Chavez has named his vice president, Nicolas Maduro, a 50-year-old former bus driver and union leader, as his heir apparent.
Opposition flagbearer Henrique Capriles, who lost the presidential race against Chavez in October, is the favorite to face Maduro should a new vote be held, though first the governor of Miranda must retain his post in local elections on Sunday.
"The regime change is already occurring," Jefferies' managing director Siobhan Morden said in one of numerous Wall Street analyses of events in Venezuela. "The question is whether the alternative is Chavista-light or the opposition."
Even if he dies, Chavez is likely to cast a long shadow over Venezuela's political landscape for years - not unlike Argentine leader Juan Peron, whose 1950s populism is still the ideological foundation of the country's dominant political party.
There are parallels with Cuba too, where Chavez's friend and mentor, Fidel Castro, suffered a health downturn, underwent various operations in secret, and eventually handed over to his brother Raul Castro.