Chavez said from Havana that he is "well on the road to recovery," Jaua said on VTV state television, after a chat in which he said the president sounded "solid, energetic and victorious."
Moments after Jaua spoke, Chavez' Twitter acount carried a message reading: "Here I go, taking off like a condor. ... We will live and we will overcome!"
Tuesday Jaua said Chavez was in good condition without offering more detail.
But he said Chavez' pelvic lesion was "totally extracted."
Venezuelan officials have never specified the kind of cancer the leftist president has, but they have denied the cancer has spread to other organs.
Cuban state TV said Chavez was operated on successfully on Monday in the Center for Medical-Surgical Research (CIMEQ), Cuba's most modern hospital.
Chavez declared himself cancer-free last October, before announcing on February 21 that a small lesion had been discovered.
The possible return of Chavez's cancer has cast doubt over his October 7 re-election bid, likely to be Venezuela's most closely contested presidential election in years.
Chavez, 57, who remains active as president while absent from Venezuela, has been in power since 1999.
The leftist firebrand now faces a strong challenge from 39-year-old Henrique Capriles, who was chosen as the sole opposition candidate in a primary earlier this month.
Chavez has used Venezuela's vast oil wealth on popular social programs and to help keep afloat his communist ally Cuba, even as he courted anti-US allies from Iran to Libya.
As during his initial cancer care in Havana last year, Chavez has not delegated power to Jaua as some opposition members sought.