Sidhu Moose Wala was killed a day after his security was scaled down.
Union Home Minister Amit Shah is expected to meet singer Sidhu Moose Wala's family in Chandigarh on Saturday.
Moose Wala's family had written a letter to Mr Shah seeking a probe by central agencies into the brutal murder of the famous Punjabi singer, according to Union Minister Gajendra Singh Shekhawat.
Moose Wala was shot dead in the Mansa district last week, a day after the new Aam Aadmi Party government pruned the security provided to the singer and about 400 other VIPs as a "temporary" move.
"Police has got vital clues regarding the murder of Sidhu Moosewala and the day is not far when we will nab the perpetrators of this heinous crime," Chief Minister Mann assured the family on Friday, a state government statement said.
Mr Mann spent about an hour with the bereaved family at Moosa village in Mansa district.
He said people who were criticising the iconic singer on various issues are now "shamelessly shedding crocodile tears" for cheap publicity.
Mr Mann said the people of Punjab are aware of their "dubious track record" and will not be misled.
Shubhdeep Singh Sidhu, known as Sidhu Moose Wala, was among the 424 people whose security was withdrawn or curtailed by the Punjab Police last Saturday ahead of the "Ghallughara week", the anniversary of 'Operation Blue Star' in 1984 to flush out militants from the Golden Temple complex.
The Punjab and Haryana High Court was on Thursday informed that the security will be restored on June 7.