Parrikar was speaking in the Goa assembly. Dawood Ibrahim, India's most wanted don considered to be an architect of the 1993 Mumbai blasts, is reportedly hiding in Pakistan.
"I don't know if anyone has the capacity to arrest Dawood (Ibrahim). The government of India has been trying this for the last 25 years," Parrikar said.
Parrikar said there was so much money involved in the illegal mining industry in Goa that the underworld would soon have been attracted to it.
"If mining illegalities had continued, then Dawood would have also come here. The kind of money involved in illegal mining would have attracted the underworld," Parrikar said.
The Supreme Court has imposed a ban on mining in Goa following on a petition filed by an environmental NGO, the Goa Foundation, represented by lawyer Prashant Bhushan.
The petition came in the wake of the tabling of the Justice Shah Commission of inquiry report, which exposed a Rs.35,000 crore illegal mining scam in Goa.