In a motion raised by Ekweremadu, the lawmakers gave INEC until December 10 to conduct the rerun elections in the state.
It was reported that the upper chamber made the call to INEC on Wednesday, November 2.
The lawmakers were said to have given the electoral body until Saturday, December 10, 2016, to conduct the re-run.
According to Channels TV, the resolution followed a motion put forward by the Deputy Senate President, Ike Ekweremadu.
Ekweremadu called his colleagues' attention to the pending elections and failure of INEC to act accordingly.
He said INEC is breaching the Electoral Act by failing to conduct the senatorial rerun election in the state.
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Also reacting to the situation, the Senate Leader Ali Ndume, said "It could be any of us as in the case of River State. Imagine a state like mine ravaged by insurgency without a representation.
"We have a new leadership in INEC and yet the cases recorded have been inconclusive elections and sometimes confusion. Today we are taking Petroleum Industry Bill #PIB deliberations without any Senator from River State."
The Chairman of the Senate INEC Committee, Senator Abubakar Kyari, however informed the Senators that the information from the Commission is that it would conduct the rerun by December 10.
The Senate, therefore, resolved to call on INEC to conduct elections to vacant senatorial seats in Rivers State not later than December 10 or Senate Plenary will be suspended.