President Buhari handed over presidential duties to Osinbajo as he left Abuja to London for a 10-day vacation.
An acting Director-General has been inaugurated for Nigeria's secret police, the State Security Service (SSS) in Abuja.
It was gathered that the sack was announced while Daura was meeting with the Acting President.
The sacked SSS boss had, along with the IGP and the Chief of Staff to the President, Abba Kyari, earlier met behind closed doors with the acting president.
Matthew Seiyefa, a director of the Department of State Services (DSS) from Bayelsa state, has been appointed as acting director-general of the service.More news: Elon Musk tweets about going private and shares 'skyrocket'
He described the "unauthorised takeover" of the National Assembly as "a gross violation of constitutional order" and "rule of law".
Several of the lawmakers, mostly from the opposition party, posted images and videos of the blockade, which happened early Tuesday morning.
Senator Rafiu Adebayo Ibrahim representing Kwara South has disclosed that lawmakers belonging to the Parliamentary Support Group, PSG, allegedly received the sum of $1 million each to impeach the Senate President, Bukola Saraki and his Deputy, Ike Ekweremadu. Parliament went on recess last week until September 25 but meetings were to be held on Tuesday.
Saraki was also expected to meet with Mahmoud Yakubu, chairman of the Independent National Electoral Commission (INEC).
"The use of armed security agents to force political outcomes does not bode well for the February 2019 general election", said Malte Liewerscheidt, vice president at Teneo Intelligence, in a note.