Thirdway Alliance Party leader Ekuru Akuot on Wednesday kicked off lobbying to persuade the 47 county assemblies to accept the Punguza Mizigo Bill.
The process is one of the requirements needed in a move to amend the Constitution.
The party leader was invited to make submissions by the Nakuru county assembly.
Aukot said the Bill will end lack of gender parity in the country.
He said the country has failed to attain gender balance as stipulated in the Constitution.
He also said the proposal to have a one-term President will end ethnicity.
Aukot said a term of seven years is enough for the elected person to bring changes.
He added that the previous chaos witnessed due to election differences will be a thing of the past.
The lawyer also said a one-term President will cut costs, saving the money which will be channeled for development.
He was accompanied by party officials.
The IEBC gave the party a go ahead last Thursday after verifying that the more than one millioin signatures collected met the threshold.
The party handed over the collected signatures on February for verification.
On Monday, Election Observer Group (ELOG) claimed that numerous signatures in the filled forms were uniform "raising the question of authenticity and reliability of the signed forms" among other irregularities that could open the process to endless litigation.
