Three candidates - BJP-backed Independent nominee Parimal Nathwani, JMM's Baidyanath Ram and Pranav Jha of the Congress - are in the fray for the two seats.
The voting started at 9 am at a polling station set up in the assembly complex amid fear of cross-voting, and will continue till 4 pm.
All NDA legislators arrived in the assembly in a bus directly from the hotel where they camped, while Congress MLAs reached the premises in a bus.
Chief Minister Hemant Soren also reached the assembly to cast his vote.
BJP chief whip Naveen Jaiswal, who was the first to exercise his franchise, said, “Twenty-one party legislators and one each from AJSU party, JD(U) and LJP (RV) cast their votes. All votes went to NDA- supported candidate Parimal Nathwani.” Nathwani exuded confidence about his victory.
"I have support from all parties, and I am assured of my victory. Everything will be clear by the evening," he said.
JD(U) leader Saryu Rai said his vote will go to the NDA-backed nominee. Asked if he is sure of Nathwani's win, Rai said, "This is not my subject. I know about my vote, which will go to him." RJD legislator Suresh Paswan claimed that there is no doubt that the INDIA bloc candidates will secure victory.
Congress minister Shilpi Neha Tirkey said they have adequate numbers and are confident of winning both the Rajya Sabha seats.
After the NDA, the INDIA bloc legislators started exercising their franchise.
"All arrangements, including adequate security, are in place to hold the polling peacefully," an Assembly official said, adding that the counting of votes is likely to commence at 5 pm.
The BJP-led NDA has 24 MLAs, four short of the minimum of 28 first-preference votes required in the 81-member assembly to secure a berth in the Upper House of Parliament.
The ruling INDIA bloc, including the JMM and the Congress, has 56 members in the House.
JMM's Baidyanath Ram is expected to win easily, as the party has 34 members in the state assembly.
Among the other INDIA bloc constituents, the Congress has 16 MLAs, the RJD has 4 legislators, and the CPI(ML) Liberation has two.
All eyes are on the second seat, in which a tough fight between Congress' Jha and NDA-backed Nathwani is likely.
The NDA's 24 MLAs include 21 from the BJP and one each from the LJP (Ram Vilas), AJSU Party and the JD(U). The Jharkhand Loktantrik Krantikari Morcha has one MLA.
Both the ruling and opposition camps were leaving no stone unturned to keep their MLAs intact ahead of the polling.
The NDA MLAs were shifted to a hotel in Ranchi on Tuesday, while the ruling INDIA bloc was busy holding meetings with its MLAs to thwart chances of cross-voting.
The INDIA bloc MLAs, including those from the Congress, participated in a mock poll during a meeting at Chief Minister Hemant Soren's residence on Tuesday night to make the new legislators aware of the exercise.
