Nearly four months after publicly admitting he was suffering from cancer, the Venezuelan president, Hugo Chávez, has claimed he is "free of the illness".

Speaking on Thursday after arriving back in Venezuela from Havana, Cuba where he has been undergoing treatment since June, the president said doctors had told him there were now "no malignant cells active in this body".

"A vital stage has been concluded. Everything went perfectly," Chávez said in a speech broadcast on state-controlled VTV.

"I got top marks, 20 out of 20," added the 57-year-old president who hopes to be returned to power in next year's presidential elections. "The tests allow me to say that I am free of the illness."

Despite being in the initial stages of a usually lengthy treatment process, Chávez was upbeat as he stepped off a plane at Táchira state's La Fría airport.

"The new Chávez is back … We will live and we will continue living," he beamed.

Speculation over Chávez's health began in June when the normally extravagant and outspoken president largely disappeared from public view, abandoning his Twitter account and his frequent and often lengthy speeches.

Then in July, after weeks of speculation about his true condition, Chávez finally admitted he was suffering from cancer. "This [is] the new battle that life has placed before us," he said during an address to the nation, which followed weeks of silence.

But Chávez's admission and his vague but regular Twitter updates about his recovery process have failed to silence the whisperers. Last month the Miami-based El Nuevo Herald newspaper claimed that Chávez had been rushed to hospital with kidney failure and was in critical condition.

In his trademark showman style, Chávez hit back at the newpapers reports, summoning journalists to the Miraflores Palace in Caracas for an impromptu game of baseball and a press conference in which he slammed the rumours as "morbid and inhumane". Chávez has yet to reveal, however, exactly what form of cancer he was diagnosed with.

Chávez's illness has prompted some onlookers and opposition figures to cast doubt on his ability to fight a successful race for office next year. But polls show the president has so far benefited from a jump in popularity, with approval ratings now running at around 60%.

On Thursday Venezuela's famously verbose leader, who has been in power since 1999, said he was confident of victory in the October 2012 presidential elections.

"To paraphrase Christ, my Lord, it will be easier for a donkey to pass through the eye of a needle than for the opposition to beat Chávez in the elections," he boasted.