The former UN boss has a sealed envelope holding the names of 10 top suspected masterminds of the mayhem that left more than 1,300 people dead, displaced 300,000 others and paralysed key sectors of the regions largest economy early last year.
Annan is to hand that envelope over to the Hague-based International Criminal Court (ICC) if Nairobi.
“I am in discussions with the two leaders … and they told me they are going to make a second attempt to get the tribunal established,” Annan told BBC radio, referring to Kibaki and Raila.
“I have also made it clear that if it is not established within a reasonable period, which I would say (is) up to the end of August, I will have no option other than to hand the envelope over with the names to the ICC”.
Dr Annan brokered the Coalition Government between Kibaki and Raila after strongly disputed presidential election results.
The names in the envelope are believed to include senior politicians and businessmen, including Cabinet ministers.
While some legislators have blocked the local court out of self-interest, analysts say, others have opposed it on grounds it would be doomed to go the way of past inquiries and fail to prosecute anyone.
Annan, however, said local justice would still be better. “I think Kenyans would be much better off with that trial taking place in their midst,” he said.
But speaking to The Standard before Annans latest ultimatum, Justice and Constitutional Affairs Minister Mutula Kilonzo said he had written to the former UN chief requesting for extension of the deadline for setting up a local tribunal.
The minister said his initiative to meet Annan was geared at “making him understand why we have taken long to form the tribunal and the challenges we are facing”.
“The deadline set for the tribunal is not as grave as the reaction from the public should the tribunal be formed without their input. We would rather delay a bit but then have blessing of all Kenyans,” said the Mbooni MP.
Report by Maseme Machuka, Beauttah Omanga and BBC