Cord on Tuesday withdrew its members from Parliament's Justice and Legal Affairs Committee.
The decision was arrived at at a Parliamentary Group meeting chaired by Cord Co-Principals Raila Odinga and Moses Wetangula.
"Cord is going to withdraw the authority of its members in the Justice and Legal Affairs Committee and directs them to stop any farther engagements in that committee," Siaya Senator James Orengo said in a statement after the meeting.
"All members of the Cord coalition withdraw from the bi-Partisan Parliamentary process on IEBC championed by a cross section members of Parliament."
The decision means that initiatives by MPs to kick-start countrywide discussions on how to solve the IEBC stand-off will stopped.
A team comprising Jubilee and Cord MPs led by Ainabkoi's Samuel Chepkonga had been scheduled to start collecting views from Kenyans on the best way to resolve the current stand-off between government and the opposition over the reconstitution of the IEBC.
The Parliamentary Group meeting resolved that only Cord-Co-Principals Raila Odinga, Kalonzo Musyoka and Moses Wetangula can select a team of parliamentarians to engage on IEBC talks.
"A pathway to dialogue on IEBC ought to be structured," Orengo said.
"That any such structured meeting will be at the highest level and that the principals of Cord will nominate those who will engage in the dialogue, reporting to the principals."
Cord before the anti-IEBC protests began had said it was ready to hold talks to find ways of reconstituting the electoral body as the country prepares for the 2017 polls.
Government however, has dragged its feet on the matter prompting the opposition to hold demonstrations aimed at forcing IEBC commissioners resign.
President Uhuru Kenyatta and his Deputy William Ruto maintain disbanding and reconstituting the IEBC can only be done within the confines of the Constitution.
The two argue that only Parliament is bestowed with powers to dissolve the electoral body.
The meeting was held at Wiper Secretariat.