The complaint was handed over to the Delhi Police, which is yet to take a call on whether to register a case or seek necessary instructions from a court for blocking the Twitter page, official sources said.
The formal complaint was sent by Rashtrapati Bhavan along with tweets posted by Lalit Modi last month.
A final call on the complaint will be taken by Delhi Police Commissioner B S Bassi, who may seek legal opinion on whether the tweets amounted to criminal defamation.
When contacted, Bassi said the complaint has been received and is being examined.
Modi had alleged that President Pranab Mukherjee, during his stint as Finance Minister, had pushed Enforcement Directorate to act against him after he had raised questions about the shareholding pattern in IPL's Kochi franchise leading to resignation of Shashi Tharoor from the Union council of ministers.