By Andrew Cawthorne

CARACAS (Reuters) - Venezuelan President Hugo Chavez's adoring supporters prayed and wept on Tuesday over a serious setback in his battle against a cancer that threatens to end his 14-year rule of the South American OPEC member.

"There is so much sadness and confusion," said one die-hard "Chavista," Marisol Aponte, a community worker in the slums of Caracas, her voice choking with emotion. "But we must be strong and put into practice all that he has taught us."

In one of the gloomiest announcements to date on Chavez's health, the government said on Monday night that his breathing problems had worsened and he was suffering from a "severe" new respiratory infection in a Caracas military hospital.

The 58-year-old president has not been seen in public nor heard from since undergoing surgery in Cuba on December 11, his fourth operation since the disease was detected in his pelvic area in mid-2011.

"God's will be done. We are just praying for him, as we have always done," said Maria Fernandez, 33, who works as a volunteer in a Socialist Party office that occupies Chavez's former home in the rural village of Sabaneta, where he grew up.

Several dozen people gathered from early morning at the Catholic chapel in the military hospital where Chavez has spent the last two weeks since returning from Cuba. Some prayed aloud, while others wept quietly.

The government has repeatedly said he is fighting for his life. Though short on medical details, officials have said he is breathing through a tracheal tube, unable to speak, and undergoing a new round of chemotherapy treatment.

The government is furious at speculation, particularly among pro-opposition media, that Chavez may already be dead. Opposition leader Henrique Capriles has repeatedly accused Vice President Nicolas Maduro and others of lying about Chavez's condition.

'WORSENING' CONDITION

Chavez suffered multiple complications after the December 11 surgery, including unexpected bleeding and an earlier severe respiratory infection that officials said had been controlled.

"Today there is a worsening of his respiratory function, related to his depressed immune system. There is now a new, severe infection," Information Minister Ernesto Villegas said on Monday night.

"The commander-president remains clinging to Christ and to life, conscious of the difficulties he is facing, and complying strictly with the program designed by his medical team."

Chavez has undergone several grueling rounds of chemotherapy and radiation treatment, which at times left him bald and bloated. He twice wrongly declared himself cured.

The only sight of the former soldier since his latest operation were four photos published by the government while he was still in Havana that show him lying in a hospital bed.

Dozens of student demonstrators have been holding protests around Venezuela, including chaining themselves up in public, to demand proof that Chavez is alive and in Venezuela.

Should the Venezuelan leader step down or die, an election would be held within 30 days and would probably pit Maduro against Capriles. Polls show Maduro is the favorite, helped by Chavez's personal endorsement as his successor.

The stakes are high, too, for other left-leaning nations around Latin America and the Caribbean. Chavez's oil-financed largess has boosted economies of allies from Cuba and Nicaragua, to Bolivia and Ecuador.

(Reporting by Andrew Cawthorne; Additional reporting by Girish Gupta and Daniel Wallis; Editing by Kieran Murray and Eric Beech)