Moi made the demand days after the Supreme Court judgement which upheld Uhuru's win.
Moi has asked Kenyatta to reach out to Odinga and make peace with him following the recent elections of August 8 and October 26 which has led to a divisive country.
"We in KANU are confident that you will rise up and extend the olive branch to those who hold political opinions contrary to yours, and in a spirit of brotherhood steer Kenya towards greater prosperity," Moi said.
While congratulating the President after the Supreme Court ruling which upheld his October 26 victory, the KANU senator advised Kenyatta to follow the footsteps of the late American President Abraham Lincoln.
"We equate Kenya society to that of America which was fragmented by civil wars of 1861 to 1865. When Lincoln won the elections he put a plan for peace and unity that was flexible and generous," Moi stated.
The senator's statement comes days after Kenyatta held a private meeting with former President Daniel Moi at Kabarak.
Kenyatta has in the recent past held several meetings with the Moi family at the former President's home in Kabarak.