He also congratulated Karnataka Chief Minister BS Yediyurappa and the state unit BJP chief for the victory.
"By giving a clear mandate to the BJP, the people of the state have rejected the selfish and the corrupt," he said, adding that results were a blow for the "divisive policies and opportunistic politics" of the Congress.
Congratulating party workers for the victory, Union Defence Minister Rajnath Singh said the people of the state have once again placed their faith on the BJP.
"The people of Karnataka have once again placed their faith in @BJP4India and CM Shri @BSYBJP. Shri @narendramodi deserves a special mention as he remains at the forefront of fulfilling people's aspirations. I congratulate the Karyakartas who worked hard for BJP's win in by-polls," Singh said in a tweet.
The ruling BJP on Monday registered a thumping victory in Karnataka by-elections, winning 12 out of 15 seats, and secured a comfortable majority in the House with the Congress managing just two seats and the Janata Dal (Secular) (JD-S) failing to open its account.