Nirmala Sitharaman also said infiltration bids from across the border with Pakistan have not come down.
Devikiamma Pillai, a South African national of Indian origin, came to India on vacation and checked in at a guest house in south Mumbai's Colaba area on February 21.
Mann, who announced his resignation on Twitter, said his fight against the drug mafia would however continue.
Punjab Congress leader Navjot Singh Sidhu on Friday said AAP convener Arvind Kejriwal had "murdered" his party in the state by apologising to SAD leader Bikram Singh Majithia.
Kejriwal tendered the apology to former minister Bikram Singh Majithia yesterday for levelling charges of involvement in drugs trade against the former minister.
The Aam Aadmi Party (AAP) unit of Punjab on Friday accused said party convener Arvind Kejriwal of becoming “weak”, a day after the latter apologised for his drug trade allegations against former minister Bikram Singh Majithia.