While the reason for his termination has not been made public, early speculations indicate that it might have something to do with DSS operatives taking over the National Assembly complex early on Tuesday.
While Idris got to the presidential villa at 12;35pm, Daura got there at 1:15pm.
It is the first such incident since Nigeria became a democracy in 1999 and coincides with increased tension between the National Assembly and the executive ahead of an election in February 2019 when President Muhammadu Buhari will seek a second term.
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The Acting President, Yemi Osinbajo, has directed the termination of the appointment of the Director General, State Security Service, Lawal Daura, with immediate effect, the presidency has said. He later left for the SSS headquarters after the meeting to take charge of the security agency.
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Police say they know some of the shootings have been random and some targeted and related to gang conflicts. The murder rate has already become an issue for Mayor Rahm Emanuel , who is up for reelection in February.
Osinbajo condemned the unauthorised standoff at the National Assembly complex, describing it as "a gross violation of constitutional order, rule of law and all acceptable notions of law and order".
Hooded armed men from the police and Department of State Service (DSS) blocked access to the two chambers - the Senate and House of Representatives - on Tuesday morning, preventing lawmakers, workers, journalists and other visitors from entering.
Saraki was also expected to meet with Mahmoud Yakubu, chairman of the Independent National Electoral Commission (INEC).
Some PDP senators, who were caught in the blockade interpreted it as a move to impeach Senate President Bukola Saraki. The DSS is a security arm that is directly under the presidency.