The approval was given at a meeting of the council presided over by President Muhammadu Buhari at the Presidential Villa, Abuja.
Minister of Information and Culture, Mr. Lai Mohammed; Minister of Power, Works and Housing, Mr. Babatunde Fashola; and the Minister of State for Aviation, Senator Hadi Sirika, briefed State House correspondents at the end of the meeting.
Fashola said work on the six federal secretariats which are in various stages of completion had been stalled since 2012.
He listed the states concerned to include Anambra, Bayelsa, Zamfara, Nassarawa, Gombe and Osun.
The minister attributed the change in costs to the change in designs, among others.
“The approved cost variation has already been captured in the 2016 budget. With the approval of the variation, we can re-mobilise workers back to site,” he said.