The 58-year-old leader -- who returned to Caracas, the Venezuelan capital, at 2:30 a.m. Monday and was rushed to a downtown military hospital after being treated in Havana for complications following Dec. 11 cancer surgery -- is now receiving palliative care after doctors determined no viable cancer treatment would improve his health, the newspaper said, citing sources in contact with Chavez's medical team.
Palliative care focuses on relieving and preventing a patient's suffering.
ABC is widely considered a newspaper of record in Spain.
The sources told the newspaper Chavez's cancer was terminal and there were no plans to bring him back to Cuba for further treatments.
A few Cuban and Russian medical specialists flew with Chavez to Caracas, while a number of specialists already left the medical team, ABC reported.
Venezuelan Vice President Nicolas Maduro said late Monday Chavez was receiving "complementary treatments for the base disease" at the heavily guarded Dr. Carlos Arvelo Military Hospital.
Information Minister Ernesto Villegas said Friday the Venezuelan leader was breathing through a tracheal tube but said Chavez's "intellectual functions" were intact and he was "in close communication with his government team."
Villegas made his comments when Caracas televised photographs of Chavez recuperating in Cuba with two of his daughters at his side. The photos showed Chavez reading Thursday's edition of Cuba's state newspaper, Granma.
By contrast, Chavez's populist government did not release photos or video images of the president's pre-dawn arrival. Nor has it said what type of cancer Chavez has had or what his prognosis is.
Chavez has had four operations for cancer since June 2011.
Fireworks were set off in parts of Caracas Monday as loyal "Chavistas" celebrated after Information Minister Ernesto Villegas called for the country to rejoice.
"El Comandante is here. He's back. He's back. He's back," Villegas almost sang on state TV.
Chavez's Twitter account, silent since shortly after he was re-elected to another six-year term Oct. 7, was suddenly active again starting at 3:42 a.m.
"We have arrived again in Venezuela," said the first of three posts attributed to Chavez after he landed. "Thank you, my God!! Thank you, beloved people!! We will continue treatment here."
Fidel Castro, the retired Cuban leader, issued a statement wishing Chavez well on his return, saying Chavez had "learned much about life" through his illness.
Maduro and government ministers participated in a mass of thanksgiving Monday night for Chavez's health, Venezuelan newspaper El Mundo reported.
Chavez, who declared himself fully recovered from his unspecified cancer July 9, 2012, flew to Havana Dec. 10 for additional cancer surgery. He later developed a severe pulmonary infection that has resulted in breathing difficulties, or a "respiratory insufficiency," the government said Jan. 3.
Chavez stirred further uncertainty when he failed to return to Venezuela for his inauguration Jan. 10. His allies insisted he was firmly in control and declared he could take as much time as he needed to recover.
The Supreme Court, which in 14 years of Chavez rule never issued a decision against the government, said the president could be inaugurated whenever he returned.
Opposition leader Henrique Capriles -- the governor of Miranda, one of the country's most populous states, which includes part of Caracas -- welcomed Chavez back but said in Twitter he hoped Chavez's return would bring "common sense" back to his government and attention to Venezuelans' daily problems.
If Chavez dies or steps down, the Constitution requires elections within 30 days.
Before leaving for Cuba, Chavez asked Venezuelans to rally behind Maduro, 50, a former bus driver, if new elections are held.