•In a statement on Wednesday, the national secretariat said the postponement was occasioned by late completion and publication of the Constitution Amendment Bill 2020.
Raila Odinga, the ODM boss, had on Tuesday announced the signature collection drive is expected to be finalised latest next week.
The BBI signature collection exercise launched which was slated for Thursday has been postponed.
In a statement on Wednesday, the national secretariat said the postponement was occasioned by late completion and publication of the Constitution Amendment Bill 2020.
The statement was signed by co-chairpersons Dennis Waweru and Suna East MP Junet Mohamed.
The two said the secretariat is working on a new date "with a comprehensive programme of rollout activities".
This comes as President Uhuru Kenyatta on Wednesday hosted his deputy William Ruto for a three-hour meeting at State House, Nairobi.
The Star understands that the two discussed the ongoing BBI debate and how Ruto's concerns can be accommodated before the process moves further.
ODM leader Raila Odinga - who is Uhuru's handshake partner - had on Tuesday announced the signature collection drive is expected to be finalised latest next week.
"On Thursday, President Uhuru Kenyatta and myself will lead the country into launching the signature collection," Raila had said.
"We want the signature collection done very quickly and by end of next week we are done with the collection."
The BBI team is expected to collect one million signatures from Kenyans, in preparation for a referendum.
The supporting signatures are then taken to the Independent Electoral and Boundaries Commission, which shall verify that the initiative is supported by at least one million registered voters.
If the IEBC is satisfied that the initiative meets the requirements, the Commission shall submit the draft Bill to each county assembly for consideration within three months after the date it was submitted by the Commission.
If a county assembly approves the draft Bill within three months after the date it was submitted by the Commission, the speaker of the county assembly shall deliver a copy of the draft Bill jointly to the Speakers of the two Houses of Parliament, with a certificate that the county assembly has approved it.
If it is approved by a majority (24) of the county assemblies, it shall then be introduced in Parliament.
On Monday, Deputy President William Ruto urged county assemblies to shun a forced 'Yes-no' campaign around BBI that he said threatens to be retrogressive for the country.
Speaking when he met Wajir MCAs, Ruto said the county assemblies must work together and push for progressive engagements around the Building Bridges Initiative.
"...so that we can build a consensus on the report. A divisive referendum process cannot be used to achieve a united country," he said.
He added: "We must at the moment prioritise the health of our people and focus on countering the effects of Covid-19."