The government also warned of action "as per the law" against the senior Congress leader if he failed to apologise.
"The Telangana Police is widely appreciated (for its professional competence). He (Digvijaya) has made a false allegation that we created something, induced Muslim children and did something. He must prove it," state Home Minister Nayani Narasimha Reddy told reporters.
"If he fails to prove it, he has to openly apologise to the police department. If he does not do that also, then action will be taken against him as per the law," he said.
"The state government would take action against him as per the law if he fails to apologise," Reddy said.
Legislator from Jubilee Hills in Hyderabad, M Gopinath, has already complained to the police on the matter, Reddy said.
"It is unfortunate that Singh, who served as the Chief Minister of Madhya Pradesh and now oversees party affairs in two states, made such irresponsible comments," the minister said.
Mr Reddy recalled that Mr Singh had made some (undesirable) comments on the Army as well.
Mr Singh, in-charge of Congress affairs in Telangana and Andhra Pradesh, kicked up a row yesterday with his remarks that the Telangana Police has set up a "bogus" ISIS website to radicalise Muslim youth and encourage them to join the terrorist outfit.
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.