Naija News reports that the former governor cited a lack of free and fair electoral process in the state as the reason for his decision.
Kwankwaso spoke while making an assessment of Saturday's supplementary election in the state.
This online news platform understands that there have been reports of widespread violence in the state, with thugs chasing voters from polling units in Gama ward, Nassarawa local government area while journalists and observers were attacked in different parts of the state.
Reacting, the Peoples Democratic Party (PDP), Nigeria's main opposition party, said it lost four of its members during the election.
In response, deputy inspector-general of police, Anthony Micheal, said the exercise had been successful despite "few incidents" of violence.
Speaking on the development, Kwankwaso said violence and rigging of the supplementary poll took place in all the 28 local governments where the election held.
His words: "It is very sad that elections could not hold today because, by yesterday evening, all the polling units in the rerun areas were overtaken by thugs. Very early morning today elections were concluded in many polling centres," he said.
"And even more concerning is the role of the police under the leadership of DIG Anthony Obizie who actually back up thugs under the leadership of the Kano state government. It is a very sad day for all of us and a very sad day for democracy.
"There are very few places where elections took place especially here in the city but there was no election in the overwhelming places because they were overtaken by thugs. People were going around with ballot papers and result sheets, writing what they wanted and submitted them to the INEC officials.
"Our prayer is that these elections should be cancelled and re-scheduled so that we can have better, free and fair elections in Kano. I don't think by all standards, the elections here in Kano can hold water. It is unacceptable and I don't think INEC can go ahead to count because there is nothing to count," he added.
Source: Naija News