However, neither of the two leaders was present in the vehicles when the incident took place.
Prima facie it has emerged that Verma's driver Naveen was driving the Toyota Fortuner on the wrong side near Vijay Chowk.
Police has registered a case of rash and negligent driving and he has been arrested.
"The incident took place around 6:00 PM when Naveen was driving the Fortuner car towards Parliament after exiting the media parking lot. Uma Bharti's cavalcade was also approaching Parliament when the SUV rammed into a gypsy which was part of the Union minister's convoy," said a police official.
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"We have registered a case against Verma's driver on the statement of the constables and he has been arrested. The SUV has also been seized and further investigation is underway," said Additional Commissioner of Police (New Delhi) SBS Tyagi.
Both the vehicles were going to Parliament to pick up the two leaders as they were leaving.
Police said that they would scan the CCTV footage of the stretch to piece together the exact sequence of events.