Hugo Chavez said the medical process had been "slow and careful Mr Chavez said he was determined to overcome his health battle and was now on the road to "full recovery".
His absence forced Venezuela to put off a regional meeting on Wednesday.
'New battle' Looking much thinner than when he last addressed the nation, Mr Chavez confirmed what many had suspected - his health problems were more serious than first thought, says the BBC's Sarah Grainger in Caracas.
Standing behind a podium, the president said he had made the "fundamental error" of failing to look after himself.
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This was a Hugo Chavez clearly weakened by ill-health. His desire to speak to the nation was undimmed, but his voice was much weaker than usual and he had visibly lost weight.
The Cuban and Venezuelan authorities have done well to keep this news under wraps for so long. But questions must be asked about whether concealing such information was the right thing to do. President Chavez addressed the issue by saying he did not want to bring his supporters on what might be an unhappy journey with him.
Venezuelans are still wondering if the president will return to the country in time for bicentennial celebrations scheduled for Tuesday. But in the longer term, his ill-health calls into question his chances of being re-elected for another six-year term in 2012.
His time spent recuperating out of the public eye has highlighted how much government is centred on him and how he lacks an obvious successor.
Analysis
The Cuban and Venezuelan authorities have done well to keep this news under wraps for so long. But questions must be asked about whether concealing such information was the right thing to do. President Chavez addressed the issue by saying he did not want to bring his supporters on what might be an unhappy journey with him.
Venezuelans are still wondering if the president will return to the country in time for bicentennial celebrations scheduled for Tuesday. But in the longer term, his ill-health calls into question his chances of being re-elected for another six-year term in 2012.
His time spent recuperating out of the public eye has highlighted how much government is centred on him and how he lacks an obvious successor.
Former Cuban President Fidel Castro had first told him he had looked unwell while he was on a state visit to Havana, he added.
Mr Chavez said he underwent a first operation on a pelvic abscess on 10 June, just as officials had informed the Venezuelan public. But during his recuperation, tests had "confirmed the existence of a tumour with cancerous cells", forcing him to undergo another operation. The extraction of the tumour had been "completely successful", he said.
He added that his condition had been "evolving satisfactorily" while he received a "complementary treatment to combat the different types of cells found, and thereby continue on the path to my full recovery".
"I deeply appreciate the demonstrations of solidarity by Venezuelans and other brotherly people," he said.
Mr Chavez called it a "new battle that life has placed before us", and ended the speech with the revolutionary slogan often used by Mr Castro: "Forever onward toward victory! We will be victorious! Until my return!"
The address was aired by the pan-American channel Telesur late on Thursday. It is unclear when it was recorded. Screen captions indicated that he was speaking from Cuba.
Afterwards, Venezuela's vice-president said the government was united and that Mr Chavez's reforms would be "deepened" despite his ill-health.
"This is not the time to go backward, it's time to advance," Elias Jaua said.
Mr Chavez did not say how much longer he expected to remain in Cuba recovering, but our correspondent says everyone hopes he will be back in Venezuela on Tuesday, when it celebrates 200 years of independence
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