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Venezuelans rang in 2013 in a somber mood as the shifting news about the health of President Hugo Chávez sank in.

The country was largely peaceful Tuesday after a New Year's Eve that saw a main government-organized celebration canceled due to Chávez's illness.

Jorge Rodriguez, a Chávez ally and mayor of a Caracas district, reiterated that the president is going through a "complex post-operative process."

He told reporters Tuesday that Venezuelans have shown an outpouring of compassion and support for a leader who has "been planted in the hearts of millions." Rodriguez urged Venezuelans to keep Chávez in their prayers and expressed hope the president would recover.

Chávez's son-in-law Jorge Arreaza, who is the government's science minister and has been with the president in Cuba, urged Venezuelans in a Twitter message Monday night not to believe "bad-intentioned rumors" circulating online. "President Chávez has spent the day calm and stable, accompanied by his children," Arreaza said in the message.

That followed a grim announcement from Vice President Nicolas Maduro on Sunday that the president had suffered new complications due to a respiratory infection that appeared after the surgery.

Bolivian President Evo Morales issued a New Year Eve greeting to Chávez lamenting the health problems plaguing his "anti-imperialist comrade."

Morales said he was sending wishes for "strength, energy, and for him to be able to recover soon." Morales made a visit to Havana last week to visit Chávez, but didn't refer to that trip.

In Bolivar Plaza in downtown Caracas, Chávez's supporters strummed guitars and read poetry in his honor on Monday night, singing along with a recording of the president belting out the national anthem.

About 300 people also filled a Caracas church for a Mass to pray for Chávez.

"This country would be terrible without Chávez. He's the president of the poor," said Josefa Carvajal, a 75-year-old former maid who sat in the pews. "They say the president is very sick. I believe he's going to get better."

Chávez's aides held a Mass as well, at the presidential palace, while government officials urged Venezuelans to keep their leader in their prayers.

Venezuelans rang in the New Year as usual with fireworks raining down all over the capital of Caracas. But some of Chávez's supporters had long faces as they gathered in Bolivar Plaza on Monday night holding pictures of the president. A government-sponsored celebration there had been called off.

Speaking to the crowd, lawmaker Earle Herrera said Chávez "is continuing to fight the battle he has to fight."

"He's an undefeated president, and he'll continue to be undefeated," Herrera said.

Political analyst Ricardo Sucre said the outlook for Chávez appeared dark. Sucre noted that Maduro appeared weary during a solemn televised appearance Sunday to announce the latest setback for Chávez.

"Everything suggests Chávez's health situation hasn't evolved as hoped," Sucre said. He said Maduro likely remained in Havana to keep close watch on how Chávez's condition develops.

"These hours should be key to having a more definitive prognosis of Chávez's health, and as a consequence to making the corresponding political decisions according to the constitution," Sucre said.

Sucre and other Venezuelans said it seems increasingly unlikely that Chávez would be able to be sworn in as scheduled Jan. 10 for his new term. The Venezuelan leader has not been seen or heard from since undergoing the Dec. 11 operation.

If Chávez dies or is unable to continue in office, the Venezuelan Constitution says a new election should be held within 30 days.

Before his operation, Chávez 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.

Chávez said at the time that his cancer had come back despite previous surgeries, chemotherapy and radiation treatment. He has been fighting an undisclosed type of pelvic cancer since June 2011.

Medical experts say it's common for patients who have undergone major surgeries to suffer respiratory infections and that how a patient fares can vary widely from a quick recovery in a couple of days to a fight for life on a respirator.

On the streets of Caracas, images of Chávez smiling and saluting were emblazoned on campaign signs and murals. One newly painted mural read: "Be strong, Chávez."

State television played video of Chávez campaigning for re-election, including one of the president shouting: "I am a nation!"

A new government sign atop a high-rise apartment complex reads: "YOU ALSO ARE CHÁVEZ."

Norelys Araque, who was selling holiday cakes on a sidewalk Monday, said she has been praying for Chávez. But, she added, "I don't think he will last long."

Araque said her family has benefited from state-run subsidized food markets and education programs started by Chávez, and that she hopes the government carries on with the president's programs if he doesn't survive.

Chávez has been in office since 1999 and was re-elected in October, three months after he had announced that his latest tests showed he was cancer-free.

Opposition politicians have criticized the government for not providing information about Chávez's condition, and last week repeated their demands for a full medical report.

Based on reporting by The Associated Press.

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