Prime Minister Abdallah Hamdok and many other political leaders have been detained, according to the nation's Ministry of Information.
Hamdok's government was formed months after the 2019 removal of Omar al-Bashir who was Sudan's president for nearly 26 years.
The 65-year-old PM said in an interview with CNN on Monday that the coup plotters are affiliated with the former president who has already been convicted and sentenced for corruption, and is in line to be prosecuted by the International Criminal Court (ICC).
21 military officers and many other soldiers were detained last month following a failed coup attempt that was also reportedly sponsored by al-Bashir's supporters.
Hamdok said on Monday his government's success with stabilising the country is making the 'old forces' nervous.
"They've always had the dream of coming back," he said.
A state of emergency has been declared by the military, but pro-democracy protesters took to the streets in Khartoum, the country's capital, demanding a reversal of the coup.
Internet services have also reportedly been cut across the country, and access roads and bridges connecting with Khartoum closed.
Early reports of a crackdown by security forces on protesters have indicated that over a dozen have been injured.
Similar coups have taken place in Mali and Guinea this year, fueling fears more might break out on the continent.