JDS will also not support a candidate of other political parties as it has 40 members in the assembly and would be short of five votes, which can be "easily managed", he told reporters here.
"We will announce the candidate of our party in two-three days," he said.
Elections would be held on June 19 for the four Rajya Sabha seats from the state.
He accused the state government for its "irresponsible" decisions and neglect of the city by newly elected BJP MPs for the garbage problem.
Kumaraswamy also said Siddaramaiah has failed to keep his promise of solving the garbage problem in six months after he assumed charge as Chief Minister.
He also flayed Siddaramaiah for imposition of prohibitory orders and arrest of the residents of Mandur for launching protest against the dumping of garbage in the village.