This is contained in a statement issued in Abuja on Tuesday by the Secretary to the Commission, Augusta Ogakwu.
Ogakwu said the election earlier moved from March 16 to July 30, 2016 was again postponed due to reports of violence.
She did not fix a new date for the re-run elections.
According to her, the incidence of violence in a number of local government areas and the atmosphere of fear and intimidation posed danger in proceeding with the election as earlier scheduled.
“This situation is now worsened by direct attacks on the commission, of which the most recent and glaring was the burning down of the INEC office in Khana LGA on July 22, 2016.
As a responsible organisation and conscious of the violence, maiming and fatalities which accompanied the previous election in March as well as developments in the state since then, the commission cannot ignore such reports.
In the circumstance, therefore, it is compelled to further postpone the re-run legislative elections in Rivers state.
One of the principal conditions earlier stipulated for the return of the state for the conclusion of the election has regrettably, not been met,” she added.
The commission, however, restated its readiness to create a level playing field for all stakeholders to participate in the electoral process.
“It has a responsibility to also ensure that voters, electoral personnel, observers and other stakeholders are not exposed to undue threats to their lives. The commission wishes to reassure all voters and stakeholders that it is ready to conclude the elections within the shortest time possible once the security situation is conducive for the conduct of peaceful polls,” she added.