“Isaias Afewerki is in robust health,” Information Minister Ali Abdu told the BBC.
He blamed the rumours, which began about a week ago, on groups wishing to destabilise the country.
Mr Isaias has led Eritrea since it gained independence from Ethiopia in 1993 – facing criticism for failing to implement democratic reforms.
Rumours on various opposition websites and on social media note that the president has not appeared on television for nearly a month, which they believe is unusual.
But Mr Ali said such concerns were “nonsense”.
“I always see him every day – I saw him today at 9 o’clock,” he told the BBC’s Focus on Africa programme.
“Isaias Afewerki is in robust health – you can put this in capital letters.”
He added that Mr Isaias was not going to go television just to “respond to this cheap propaganda”.