The Telugu Desam Party (TDP) will back Congress leader BK Hariprasad, the opposition candidate for the election to the post of the Rajya Sabha's deputy chairman, the party said on Wednesday.
The NDA's candidate is Harivansh Narayan Singh of the JD(U) for the election.
"We have decided to support Congress leader BK Hariprasad," TDP leader YS Choudhary said.
The TDP has six members in the Upper House.
The party had moved the no-confidence motion in the Lok Sabha in July against the Narendra Modi government.
The current strength of the Rajya Sabha is 224 and support of 123 members would be required for a win in the full house.