Both Mandya and Bangalore Rural seats were held by JDS in its heartland.
The Congress swept to power in the May assembly polls and JDS had fought an acrimonious and bitter battle.
The BJP had backed JDS candidates in the two segments, where bypoll was necessitated following the resignation of N Cheluvarayaswamy (Mandya) and Kumaraswamy (Bangalore Rural) who quit after being elected to the assembly in May.
Suresh is the brother of senior Congress leader and MLA DK Shivakumar.
Mandya is a bastion of JDS, which won five of the eight assembly seats in the district in the May elections.
In Bangalore rural, where Kumaraswamy had won by 1.3 lakh votes in the 2009 Lok Sabha polls, the Congress has secured the support of Samajwadi Party MLA, CP Yogeeshwara, who had defeated Anita Kumaraswamy in the May polls.