The cases have been referred to the Crime Branch of Delhi Police for investigation.
Three cases have been registered at New Usmanpur police station under North East district in connection with the incidents during the inauguration of the Signature Bridge, Delhi Police said in a statement.
"All the three cases are being referred to crime branch for further investigation," the statement said.
The state BJP president alleged in his complaint that Khan pushed him down and threatened to shoot him.
Earlier in the day, Delhi Home Minister Satyendar Jain had directed the Additional Chief Secretary (Home) Manoj Parida to lodge a police complaint against Tiwari for allegedly indulging in violence at the Signature Bridge inauguration.
In his note to Parida, Jain said Tiwari and his associates indulged in hooliganism to overawe the highest functionaries of the government at the event where Chief Minister Arvind Kejriwal and other cabinet ministers were present.
"Manoj Tiwari and his associates formed unlawful assembly, forcibly entered (reached the) dias with the intention to attack and harm the chief minister and council of ministers and create ruckus, obstructed and assaulted public servant..." Jain said in the note.
"It is therefore directed that home department immediately lodges a formal complaint with the CP (commissioner of police) and concerned DCP/police station against Manoj Tiwari and his associates..." he said.
Jain said a CD containing various videos of the event showed the "lawlessness" Tiwari and his associates indulged in.
He said the police in the country, particularly in Delhi, worked under "tremendous political pressure".
Earlier on Tuesday, BJP leaders and workers staged protests across Delhi, demanding Khan's arrest and waved black flags at Kejriwal in Nand Nagri, where he had gone to attend an official function.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)