CBI sources said a case has been registered against Singh, Qureshi, his employee Aditya Sharma, owner of Trimax group of companies Pradeep Koneru and other unknown persons.
They said the agency conducted searches in four cities-- New Delhi, Ghaziabad, Chennai and Hyderabad.
Qureshi has been accused of accepting money from several people for securing favours from public servants.
The FIR was lodged on a complaint from the Enforcement Directorate, the country's anti-money laundering probe agency.
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The CBI has based its FIR on the complaint forwarded by
the Enforcement Directorate chief Karnal Singh, who alleged that in the course of investigation in a Foreign Exchange Management Act (FEMA) case against AMQ Group of companies owned by Qureshi, it transpired that the businessman was acting as a middleman for some public servants.
In his letter, the ED chief attached records of Blackberry chat messages exchanged between Singh and Qureshi to allege that cognizable offences were committed by the two in collusion with each other.
The ED has appended 22 BBM messages which were exchanged between AP Singh and Moin Qureshi even after the retirement of the IPS officer.
Only three messages, in addition to 22, were allegedly exchanged between Singh and Qureshi when the former was the CBI Director, according to the ED.
The message listed by Enforcement Directorate, during Singh's tenure as CBI Chief, in its complaint are as follows:
Singh, responded after seven hours, writing, "Checked. Charge sheet already filed. Now he has to approach courts for relief."
CBI has booked Singh, Qureshi and others under sections
related to criminal conspiracy and provisions of Prevention of Corruption Act.
The ED has also attached with its complaint 18 BBM messages allegedly exchanged between Moin and Raghini Brar, daughter of Singh.
"The data record including BBM messages obtained from Income Tax contain various nefarious transactions indicating therein that Qureshi has been liaisoning and obtaining illegal money from various public persons for getting their work done, through public servants.
"Besides, these public servants have also obtained illegal gratification/pecuniary gain either themselves or by their relatives," it alleged.
The ED has alleged that Qureshi, through a company named India Premier Services Pvt Limited, applied for obtaining a concession agreement from Delhi International Airport Limited for running lounge services at Terminal three.
The ED claimed it also intercepted conversations and BBM messages between Qureshi and accused in various cases seeking undue favours from the government.
The anti-money laundering agency claimed it was evident that he was able to get "undue relief" for such accused in the cases being probed by investigating agencies and others seeking favours. Qureshi was also alleged to have obtained "huge amount of money" for the work done.
It gave a list of seven properties belonging to Qureshi in London (2), Dubai (3), New York and Singapore which were not declared in his Income Tax returns.
The ED alleged Qureshi used his ill-gotten wealth to acquire properties outside India.