Reports from Eritrea say a group of soldiers have surrounded the ministry of information building in the capital, Asmara.
State TV was off air for several hours but was broadcasting again by the evening.
The city is said to be calm with no shots having been fired.
Eritrea's government has been criticised by human rights activists as one of the world's most repressive and closed countries.
The websites of key Eritrean state and ruling party media have been operating erratically, with the site for the ruling People's Front for Democracy and Justice (PFDJ) party inaccessible for part of Monday.
A statement was reportedly read out in the early afternoon on state radio and television calling for the implementation of the country's 1997 constitution.
However, when state television resumed normal transmission with a delayed news bulletin at 21:45 local time (18:45 GMT), there was no comment on the incident.
The UK Foreign Office said that it had received reports of "unusual military movements in and around Asmara", and noted that local radio and TV appear to have been shut down.
President Isaias Afewerki has ruled the country as a one-party state since independence from neighbouring Ethiopia in 1993.