A decision to the effect was taken as per the directives of the party's Central leadership, state BJP president K Laxman said in a statement.
Election would be held to fill three vacancies and four candidates, three belonging to TRS and one Congress nominee, are in the fray.
TDP's Telangana unit said yesterday that it would not take part in the Rajya Sabha election.
With the BJP and also TDP deciding to stay away from the election, the TRS is expected to wrest the three seats as its ally AIMIM has announced support to the party.
In the 119-member Legislative Assembly, the party-wise strength is: TRS-82, INC-19, MIM-7, BJP-5, TDP-3, Independent-1, CPI(M)-1 and CPI-1.
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