Vashishth was shot in central Delhi’s Rajendra Place area on Saturday.
Vashishth’s family members, including his wife Priyanka, met Rajnath Singh at his residence here on Monday, demanding an inquiry into the incident.
After the meeting, Priyanka said the home minister assured them of a fair probe into the incident.
“We met the home minister. He was very helpful and told us that a Special Investigation Team (SIT) has been set up to look into the matter,” Priyanka said.
“He told us that there has been no justice towards us and we are convinced by what he said. He also assured us that he will be willing to help us in the future,” she added.
Vashishth’s kin have termed the incident a staged shootout.
According to police, Vashishth had more than 50 cases of attempt to murder and cheating registered against him in Delhi, Mumbai and Chandigarh.
Police also claimed that Vashishth along with his wife and father-in-law was wanted in a case of cheating registered by the Economic Offences Wing (EOW) of Delhi Police.
Vashishth, a resident of west Delhi’s Patel Nagar, hailed from Uttar Pradesh’s Baghpat city.