The video was also posted on the ODM party Twitter handle.
In a letter to NCIC chairman Samuel Kobia, UDA Secretary General Veronica Maina wants Junet and Joho compelled to acknowledge they deliberately deceived Kenyans.
However, the duo had pulled down the videos from their timelines by yesterday.
"We implore your office to act immediately and take action with a view to take down the unlawful videos as well as suspend the respective accounts propagating hate speech," said Ms Maina.
The letter has also been copied to the Communications Authority of Kenya and the Independent Electoral and Boundaries Commission.
Social media platforms have been encouraged to flag hate content to avert violence during the August 9 General Election.
Last week, NCIC gave an ultimatum to Facebook for allegedly failing to filter hate messages on its platform.
The commission said should Facebook fail to stick to anti-hate guidelines, it might be suspended from Kenya.
However, Interior Cabinet Secretary Fred Matiang'i and ICT's Joe Mucheru dismissed the NCIC's proposal, saying the government would not infringe on the people's right of expression.
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