"A phone call? What phone call? There is nothing like that," an MP allied to Ruto but who did not want their identity revealed because they are not authorised to divulge details about the president-elect, said.
Ruto's spokesman Emmanuel Talam said he was not in a position to know if the two leaders had been in touch.
On Monday evening, President Kenyatta sent out a recorded message in which he congratulated the election winners, assured of a smooth transition, and issued an oblique attack on the Supreme Court and the Independent Electoral and Boundaries Commission.
The electoral agency had been accused of bungling the presidential election, but the seven-judge apex court dismissed all petitions challenging Ruto's win.
The silent treatment between the two leaders has persisted, with no indication of who will be the bigger man and break the ice.
President Kenyatta had backed Raila Odinga- his rival in the past two elections- to succeed him and warned against electing his deputy, Ruto, describing him as unfit to lead.
On Monday, Ruto said that he had not made any demands on Uhuru and understood that the president was free to back whoever he wanted.
"When I chose Uhuru Kenyatta, I did not give him any conditions. So I take no offence at all that he chose to support another person. And therefore, we will remain friends in the context of where we are," he said.
Uhuru's feelings about handing the keys to State House to Ruto are well documented.
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If there was suspicion that Uhuru would not be amendable to receiving a phone call from the president-elect, it was confirmed by his recorded message that avoided mentioning Ruto by name or congratulating him.
In contrast, world leaders were quick to offer congratulatory messages to the president-elect.
Uhuru's message, on the other hand, appeared to suggest that he was dissatisfied with the top court's judgement.
"We must ask ourselves, is it about numbers or is it about the process? Which of these two is it? And can our institutions rule one way in one election and another way in another election without scrutiny?" he posed.
This was in reference to the nullification of his and Ruto's election in 2017 after a successful challenge by Raila, which resulted in a repeat election.
The outgoing president, however, promised to ensure the transition process proceeded smoothly. "When I was sworn in as your president, I made a pledge to the country. I pledged to uphold the rule of law and decisions made by the Judiciary on all matters of our government. Today, the Supreme Court made a ruling on the presidential dispute upholding the results announced by the IEBC on August 15. I commit to executing the orders of the court to the letter."
The very public cold war between Uhuru and Ruto is in stark contrast to the transition of power witnessed when President Mwai Kibaki vacated office in 2013.
Even before the dust had settled on the election, and the Coalition for Reforms and Democracy had filed a petition to challenge results of the presidential election, President-elect Uhuru Kenyatta and deputy William Ruto were invited to State House where they were hosted by Kibaki.
Kibaki showed the Jubilee duo around, and a statement issued later said the outgoing president had wished them success as they embarked on the journey of serving the nation.
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