* President suffering post-surgery complications
* Socialist leader diagnosed with cancer in mid-2011
* Chavez has not been seen, heard from in three weeks
By Daniel Wallis
CARACAS, Dec 31 (Reuters) - Venezuelan President Hugo Chavez is in stable condition and spent Monday with his daughters, the cancer-stricken leader's son in law said in an appeal for supporters to ignore rumors about his condition.
Chavez has not been seen in public nor heard from in more than three weeks. The vice president said on Sunday that the 58-year-old was suffering a third set of complications after surgery in Cuba on Dec. 11, his fourth operation in 18 months.
"Compatriots, DON'T believe in ill-intentioned rumors," Science Minister Jorge Arreaza, who is married to Chavez's daughter Rosa Virginia, wrote on Twitter from Havana where they have been at the former soldier's bedside.
"President Chavez spent the day quietly and stable, together with his daughters."
Chavez has not provided details of the cancer that was first diagnosed in June 2011, leading to speculation among Venezuela's 29 million people and criticism from opposition leaders.
Officials have said he suffered unexpected bleeding as result of the complex, six-hour operation on his pelvic area, and that doctors had to fight a respiratory infection, which then caused his latest setback on Sunday.
The government has repeatedly described Chavez's condition as "delicate," warning Venezuelans to prepare for difficult days ahead and urging them to pray for "el Comandante."
The main New Year's Eve party in downtown Caracas was canceled. Instead, the information minister hosted a smaller gathering which featured musicians, speeches and prayers and was dubbed "Now More Than Ever With Chavez."
The president's death or resignation due to illness would upend politics in Venezuela, where his personalized brand of oil-financed socialism has made him a hero to the poor majority but a pariah to critics who call him a dictator.
His condition is also being watched closely around Latin America, especially in other leftist-run nations such as Cuba, Ecuador and Bolivia, which depend on subsidized fuel shipments and other Venezuelan aid for their fragile economies.
In his New Year's message, Bolivian President Evo Morales said the region's leaders were missing Chavez badly.
"We feel that there has been a tremendous absence, especially for the presidents like us who are anti-imperialist and anti-neoliberal," Morales said.
"We are convinced that with the great will of Bolivia's people, all the world's people who pray, who do rituals to Mother Earth for his health, our brother president will be there soon. This is our great wish on the last day of 2012."
Chavez is due to be sworn in again in Venezuela on Jan. 10 after he won re-election in October. But top officials from his ruling Socialist Party (PSUV) have suggested the ceremony could be pushed back if he were unable to return.
For the opposition, any postponement would be just the latest sign that Chavez is not fit to govern and that new elections should be held to choose his replacement.
If Chavez had to step down, new elections would be called within 30 days and his newly named heir apparent, Vice President Nicolas Maduro, would be the PSUV candidate.
Maduro has tried to copy Chavez's bombastic rhetoric in speeches during the president's absence, but he has struggled to replicate Chavez's extraordinary man-of-the-people charisma.
Opposition figures believe they would have a better chance against Maduro than against the president, who for 14 years has appeared almost unbeatable at the ballot box.
Henrique Capriles, the opposition leader who was beaten by Chavez in the presidential election in October, said in a year-end message that Venezuelans needed to unite.
"Everything indicates that 2013 will be a tough year with big changes," he said. "Venezuela has learned a lot in very little time. Today we know the value of union, of agreement, of the need to find common ground and work together to achieve it."
Polls conducted before October's vote - well before Chavez named him as his successor - showed Capriles would beat Maduro.
But it could be a very different story if a new election were to be called now, with the vice president expected to be carried on a wave of emotion from distraught Chavez supporters.
As the New Year approached in Caracas, many PSUV loyalists retweeted a message that read: "In 2012 I cried with Chavez, loved with Chavez, voted for Chavez, laughed with Chavez and prayed for Chavez. In 2013, I will continue to be with Chavez."