Tuju did not give reasons for the postponement of the polls were earlier scheduled for Monday.
This came amid speculation of ongoing talks between aspirants Mike Sonko and former Gatanga MP Peter Kenneth.
Sources within the party intimated that the negotiations for consensus between Sonko and Kenneth are still ongoing.
The two are among candidates seeking to fly the Jubilee flag in the race against incumbent Evans Kidero of ODM.
Former Starehe MP Margaret Wanjiru is also eying the ruling party’s ticket ahead of the August 8 polls.
The three were initially in the Team Nairobi which also had Nominated MP Johnson Sakaja and Dagoretti South MP David Waweru.
Sakaja will contest the senator seat whereas Waweru will defend his seat during the general election.
On the postponed Nairobi polls, Tuju said that they initially planned the exercise for Tuesday but realised they can run alongside those of ODM.
“Jubilee is not seeking an extension of time for party primaries beyond Wednesday,” he told journalists on Sunday.
“All ballot papers have been printed. We are prepared for the nominations.”
President Uhuru Kenyatta on Saturday apologised for the chaos witnessed during Jubilee party primaries on Friday.
He said the party did not anticipate the large turnout of voters during the primaries which were cancelled following the confusion.