Thabo Mbeki, the president of South Africa, said he had been informed by the executive-secretary of the Southern African Development Community (SADC) that Mwanawasa had died.
Mwanawasa was rushed to hospital on Sunday in the Egyptian resort of Sharm El-Sheikh after suffering a stroke just before an African Union summit.
He was later transferred to Paris for treatment.
But Banda said Mwanawasa was being treated for hypertension.
"The doctors attending to [Mwanawasa] are happy with progress he has made so far and his condition remains stable. He has continued to receive treatment for hypertension in the intensive care unit and there are no new developments," he said.
In France, questioned on reports that the president had died, Frederic Desagneaux, a French foreign ministry spokesman, said: "No, I am not in a position to confirm it."
He added: "I confirm to you ... that ... Mwanawasa is currently being cared for at the Percy-Clamart military hospital."
He said it was for the Zambian authorities to give updates on his condition.
Mwanawasa chairs the South African Development Community (SADC), which has been acting as mediator between Robert Mugabe, the Zimbabwean president, and the opposition to try to end a political and economic crisis in the country.
He has also been an outspoken critic of Mugabe and his handling of his country's affairs.