The BJD won 103 seats in the 147-member assembly in 2009 elections, leaving behind the Congress and BJP with only 27 and six seats respectively.
The opinion poll conducted by private television channel NDTV gives Patnaik's BJD 13 Lok Sabha seats, one less than what it won in the last elections. It predicted just one seat for the Congress.
The BJP said it will bag a sizable number of assembly seats. It believes a government in the state cannot be formed without its support.
The ruling party discounted the opinion poll and said it expects to win 18 Lok Sabha seats and over 100 assembly seats. The BJP said it will get more than what was projected, while a Congress leader said his party may get three-four Lok Sabha seats and retain its assembly seats.
"Narendra Modi factor is not working in Odisha. Some may tilt towards Modi, but this may not be enough to fetch BJP a seat. We will get 18 seats, four more than what we got in the last elections," BJD vice president and Minister Surya Narayan Patro told IANS.