Three Commissioners resigned on Monday morning blaming Chebukati's poor leadership.
Taking his order to Twitter on Monday, Mr Murkomen, a confidant of DP William Ruto, told two other commissioners Mr Molu and Guliye to leave office alongside the chairman in what seems a bitter turning point for the troubled Commission.
“Chebukati, Molu & Guliye must resign from IEBC within the next 7 days or we form a Tribunal to investigate them,” he tweeted, minutes after the three Commissioners - Connie Maina, Margaret Mwachanya and Paul Kurgat - resigned from IEBC.
The conflict at the IEBC boiled over after half of the current commissioners resigned "with immediate effect".
IEBC Vice chairperson Connie Nkatha Maina and Commissioners Margaret Mwachanya and Paul Kurgat said they had left the commission because they had no faith in chairman Wafula Chebukati's leadership.
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The commission, which has been at war since the lead-up to August 8, 2017 elections, has become dysfunctional due to external interference, the commissioners said in a statement read by Ms Mwachanya.
"The chairman has, in several instances, failed to be the steady and stable hand to steer the commission ship," the three commissioners said.
"This race to chase ghosts that do not exist must stop. We must banish the external players from the commission boardroom, and regain the independence of the commission."