The Acting President said the invasion was carried out without the knowledge of the Presidency.
Operatives of the Department of State Services (DSS) took over the complex early on Tuesday and prevented lawmakers and journalists from gaining access into the premises in what many believe to be a plot to implement the impeachment of Senate President, Bukola Saraki.
According to a statement signed by Osinbajo's spokesperson, Laolu Akande, the "unauthorized takeover" of the legislative complex was done without the knowledge of the Presidency as alleged by the opposition.
The statement read, "Acting President Yemi Osinbajo, SAN, has described the unauthorized takeover of the National Assembly complex earlier today as a gross violation of constitutional order, rule of law and all accepted notions of law and order.
"According to him, the unlawful act which was done without the knowledge of the Presidency is condemnable and completely unacceptable.
"By this statement, Professor Osinbajo is consequently assuring Nigerians that all persons within the law enforcement apparatus who participated in this travesty will be identified and subjected to appropriate disciplinary action."
Shortly before releasing the statement, Osinbajo sacked Lawal Daura as the Director-General of the DSS and ordered him to hand over to the agency's most senior officer until further notice.