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The Inspector-General of Police, Ibrahim Idris, had invited the Senate President to answer questions on his alleged links to the criminal gang that carried out the Offa robbery attack that led to the death of 33 people in April.
In response to the summon, Saraki had said that it was a political persecution but promised to honour the invitation on Tuesday morning.
Videos have emerged on social media showing several police trucks blocking the Senate President's convoy in his neighbourhood.
When contacted for comments, the Senate President's media aide, Olu Onemola, told Pulse Nigeria, "No comments. The videos are self-explanatory."
While Saraki was scheduled to meet with the police by 8am, officers were reported to have blocked his residence at dawn.
Uche Anichukwu, the media aide to Deputy Senate President, Ike Ekweremadu, told Premium Times that the lawmaker is also under siege by security agents, for unexplained reasons.
Police officers and operatives of the Economic and Financial Crimes Commission (EFCC) laid siege to Ekweremadu'sresidencelocated at Apo Legislative Quarters, Abuja.
"The house is currently surrounded by security agencies since early in the morning," he said.
UPDATE
Saraki condemns actions of security operatives
It's unclear how the Senate President made it out of his residence, but he appeared at the National Assembly and presided over the day's session.
While speaking during Tuesday's plenary, the Senate President said he decided to chair the day's session after Ekweremadu called to inform him that he couldn't leave his house to deputise for him while he honoured the police invitation.
He said, "As you know the seat of the DSP, Ike Ekweremadu is absent. He cannot get out of his house. He is being held under seige.
"This morning I could not also leave my street as well because some people believed today's seating must not hold because some members want to move or defect.
"This is not something that started today. It will not end today. People have gone and come back, but these types of actions do not allow for such.
"As we are speaking, our DSP cannot leave the house. We must save this democracy. People have free association. They can even move tomorrow. I am sitting here and 16 members have decamped or defected to one party to another and there has been no seige.
"I don't believe that this should come to this level where people would be laid under siege for something that is personal to them."
EFCC questions Ekweremadu over money laundering
Reports later emerged that the EFCC questioned Ekweremadu over allegations of money laundering, conspiracy and abuse of office.
In a letter of invitation, dated July 24, the EFCC asked the lawmaker to show up at its office by 10am on Tuesday, the same day the letter was issued.
The letter read, "The commission is investigating the above mentioned case in which your name featured prominently and the need to obtain clarifications from you became imperative.
"In view of the above, you are kindly requested to report and interview the undersigned at 5, Famela Street Off Adetokunbo Ademola Crescent Wuse II, Abuja on Tuesday 24th July, 2018 at 10am prompt.
"This request is made pursuant to section 38 (1) of the Economic and Financial Crimes (Establishment) Act, 2004."
In a statement signed by Ekweremadu's Special Adviser on Media, Uche Anichukwu, early on Tuesday, he said the lawmaker was never invited until the morning siege.