“There has been a failed coup attempt, the people should confront it,” state media reported, but did not identify the plotters.
Reports from the capital city Khartoum and nearby Omdurman say there has been intense military activity, and bridges across the River Nile have been closed.
The plotters had tried to take over the state media building, AFP news agency quotes a government source as saying.
Video on social media appears to show armoured vehicles on city streets.
The government is reported to have said measures are being taken to contain the situation.
According to Reuters news agency, military spokesman Mohamed Al Faki Suleiman says the interrogation of suspects will soon begin.
Two years ago, the country’s long-term ruler Omar al-Bashir was toppled. A power-sharing agreement then established a government involving the military, civilian representatives and protest groups.