Levy Mwanawasa remains in intensive care in Paris
Zambia's main opposition party has called for a medical investigation to determine whether President Levy Mwanawasa is fit to lead the country.
Opposition Patriotic Front (PF) leader Michael Sata said people did not believe government reassurances the president was in a stable condition.
Mr Mwanawasa, 59, is in a Paris hospital after suffering a stroke at a recent African Union summit in Egypt.
Officials have angrily denied South African reports he had died.
PF leader Michael Sata told local radio the government should appoint a medical team to travel to France and investigate the ailing president's condition.
"The nation wants to know the truth. Nobody believes the statements being given by government," Mr Sata is quoted as saying by the AFP news agency.
But the government has dismissed the calls, saying any transition must follow the law as stipulated in the country's constitution.
The president is on the mend and will resume his duties soon, the government says.
But political analysts, opposition figures and a senior member of the ruling Movement for Multi-party Democracy (MMD) have pressed the government to initiate a transition to avoid creating a leadership crisis.
The BBC's Musonda Chibamba in Lusaka says many Zambians doubt that he will be able to do so and want concrete information on how soon the leadership vacuum can be filled.
"Even if we are confronted with a problem, we must remember that the selection of a leader must be a democratic process," Information Minister and government spokesman Mike Mulongoti said.
Mr Mulongoti said the MMD's constitution governs the election of a party leader and warned against acting out of panic.
"We have provisions in the constitution. We are being ably guided by the attorney-general. If there's anything that goes wrong, we'll consult the attorney-general and the chief justice," he said.
Mr Mulongoti also sought to allay fears over a possible transition, saying the government has "sufficient capacity and tenacity" to deal with such a process.
President Mwanawasa has undergone an operation to improve his breathing, and is in intensive care at the Percy military hospital.
His health has always been an issue during his presidency.
In April 2006 he suffered a minor stroke four months before general elections.