However, the officials haven't said what is afflicting Zenawi, bikyamasr.com reported Friday.
Most reports indicate Zenawi, 57, is gravely ill, but little else is known about his malady.
Newspapers have been barred from reporting on his health condition and Ethiopians also are forbidden to discuss Zenawi's health, sources told bikyamasr.com.
However, Ethiopian Satellite Television, based in Amsterdam, Netherlands, reported Monday the prime minister had died, saying its report was based on information from the International Crisis Group, a Brussels-based think tank. The think tank said statement it had "no direct knowledge" of Zenawi's condition.
Zenawi has ruled Ethiopia since a coup in 1991.
Many in the country, especially the activist youth, say they're wondering what Ethiopia would be without Zenawi.
"It will definitely be interesting to see how we all react," one activist told bikyamasr.com said. "Ethiopia will be better when we all, Christians and Muslims, work together to build a country based not on one group dominating the other, but on the idea that we can have a solid country for all Ethiopians."
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