The government of the pariah state blames the lies on the U.S. Central Intelligence Agency (C.I.A.), among others.
Isaias Afwerki is in robust health, Information Minister Ali Abdu said to the BBC.
The speculation began about a week ago, when opposition websites and social media outlets pointed out the president has not been seen on television for almost a month, the BBC reports.
The President will not appear on television simply to respond to this cheap propaganda, however, Ali added.
Isaias, 66, has been president since the country gained independence from Ethiopia in 1993, after 30 years of conflict. The two countries fought a border war from 1998-2000 that claimed upwards of 70,000 lives and have remained at odds ever since.
State television aired a special broadcast Sunday in response to the rumors, insisting that Isaias is in remarkable health, and went so far as to include various images of the president out and about and meeting with citizens.
We would like to announce that President Isaias is fit as a fiddle and is in the best of health under all criteria, Reuters reports the broadcast as saying.
Eritrea has long felt that the U.S. supports Ethiopia in the border disputes between the two Horn of Africa nations.
The fact that the source of this fairytale is none other than ... the Central Intelligence Agency could not even deceive the naïve, Agence France Presse quoted a government statement.
The mystery surrounding Isaias' health comes after Ethiopian forces crossed into Eritrea and attacked alleged rebel bases in March -- the first such move since the 1998-2000 war. Eritrea and Ethiopia both claim their rebel groups are receiving assistance from the other nations.
It is unknown who would assume power in the event of Isaias' death. Opposition groups claim Isaias is preparing his son to succeed him, however U.S. diplomatic correspondence published by WikiLeaks indicate the military may try to take control, Reuters reported.
The United Nations has maintained sanctions against Eritrea for harboring Islamist militants, including Somali al-Qaeda cell al-Shabab, since 2009.