The resignation of Hailemariam, in power since 2012, comes amid protracted anti-government protests and follows a nationwide state of emergency past year.
Quoting an unnamed source "close to the government", the Addis Standard newspaper reported that the Council was debating whether to make the measure span three or six months.
A day later, and the government has declared a new state of emergency.
Hailemariam, 52, has served as prime minister since September 2012.Speaking on state television Thursday, he said he is stepping down "to be part of the solution and for the success of the reforms and the solutions we have put in place".
Details of parts of the civilian constitution to be suspended will be announced at the end of the ministerial council's meeting, but it is likely to be not much different than the October 2016 nine month state of emergency, which was extended by additional four months.
Anti-government protests in the country began more than two years ago, mostly in Oromia and Amhara regions.
Protesters had blocked roads leading out of Addis Ababa, Ethiopia's capital, with rocks and burning tyres, disrupting public transportation in the city. It was unclear how soon he would vacate the office and who would replace him.
The US embassy statement said that "the challenges facing Ethiopia, whether to democratic reform, economic growth, or lasting stability, are best addressed through inclusive discourse and political processes, rather than through the imposition of restrictions".
A day before his resignation, he presided over a massive prisoner amnesty that saw detained politicians from the Oromo ethnic group freed along with hundreds of other prisoners.
A member of the Wolayta ethnic minority in the country's south, Hailemariam was seen as lacking the charisma of his predecessor Meles Zenawi, who led the EPRDF to victory over the Derg communist Junta. "So the change of an individual is really the homework for the EPRDF, not the people of Ethiopia".
Thousands of prisoners were since pardoned or released from custody, including some of the country's most prominent dissidents.