Daura, who was appointed to the post by President Muhammadu Buhari in 2015, was axed over the invasion of the National Assembly Tuesday morning by masked officials of the SSS, an incident the presidency said was not authorised.
Seiyefa was also the Director, Institute of Security Studies, Abuja. He declined to speak to newsmen.
Lawmakers loyal to Buhari's All Progressives Congress (APC) are believed to be planning to oust the president of the Senate, Bukola Saraki.
This information was disclosed on Tuesday by a media aide to the Senate President, Bamikole Banks Omisore, via a tweet.
Seiyefa is native of Bayelsa State.
It is not clear if the meeting scheduled for Tuesday afternoon will still hold after today's turn of events.
"The chairman of APC is now meeting with some APC senators".
Seiyefa, who came out of the Acting President's office around 5p.m, left the Villa in another auto.
A statement by the NBA President, Abubakar Balarabe Mahmoud (SAN) said, "The Nigerian Bar Association condemns this brazen and blatant act of the security personnel and demands the immediate withdrawal of this personnel".
Adding that he would move to have their visas revoked by western nations for their anti-democratic moves.
Nigeria's senate minority leader has resigned from his position amid speculations he might officially defect from the opposition party to the ruling party on Wednesday.
The resignation letter, dated 4th August 2018 however did not state any reason for the resignation.
The operatives turned away cars of lawmakers and other National Assembly staff.
In one of the videos, he is seen with Hon.
Saraki was also expected to meet with Mahmoud Yakubu, chairman of the Independent National Electoral Commission (INEC).