Only three are in office — Mr Wafula Chebukati, Prof Abdi Guliye and Mr Boya Molu—following the resignation of four others.
The selection panel that recruited the current team was dissolved and MPs are haggling over the membership of a new team.
The new laws are also necessary to enable IEBC conduct a referendum.
Mr Muturi has asked the newly reconstituted Justice and Legal Affairs committee to prioritise the proposed laws.
Members of Parliament are racing against time to enact electoral laws to guide the conduct of a referendum, appointment of poll commissioners and procurement of election equipment.
Among the pending Bills is one to establish a procedure for recruitment of Independent Electoral and Boundaries Commission (IEBC) commissioners.
