Armed men wearing the black uniform of the Department of State Security (DSS) stood at the gates of the building in the capital Abuja and were later joined by police officers, witnesses said.
Seiyefa, who hails from Bayelsa State, was before his new appointment the most senior director in the DSS - assistant DG.
Akande is yet to give further details on Daura's sack, however, the development may not be unconnected to the blockage of the National Assembly by operatives of the DSS.More news: Gates tells Manafort trial he assisted in filing false tax returns
Recall that Senate President Bukola Saraki had called for a leadership meeting of the national assembly.
Nigeria's acting president Yemi Osinbajo has fired the head of the country's intelligence agency, according to Osinbajo's aide, after masked security men prevented lawmakers and staff from entering the country's parliament earlier in the day.
The statement came shortly after Daura left the office of the Vice President.
Mr 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".