"I am cheering for success of Kenya", Tillerson said, noting that the two leaders' meeting will "make positive contribution" to efforts of healing Kenya's post-election tension.
Tillerson praised Kenyatta for reaching out to opposition leader Raila Odinga, saying that was a major milestone in consolidating national unity.
Talking about their planned meeting on social media, the former SONU leader Babu Owino urged their supporters attending the meeting to be ready for anything, purporting that the meeting could as well not end so well.
Speaking after the rare and historic meeting, Odinga told reporters: "The time has come for us to consult and resolve our differences, these differences are becoming too entrenched, people are dying out of these differences".
Kenyatta said they "have a responsibility as leaders to find solutions".
"This is a purely domestic initiative", Mr Odinga's spokesman Dennis Onyango said.
"The US is glad to see Kenya building investor confidence because that will help in the growth of the economy", the US Secretary of State stated.
The 73-year-old doyen of Kenyan opposition politics lost the presidential contest to Kenyatta during the August 8 2017 polls that were later nullified by the apex court over gross malpractices.More news: Kentucky cruises past Georgia to advance to SEC tourney semis
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Before the Friday meeting, the two men had defied calls from Kenyan civil society, religious leaders and western diplomats to hold talks to overcome deep divisions opened up by the disputed elections.
Odinga said the opposition had made a decision to change tactics for the sake of the country's unity.
Madaxweynaha Kenya Uhuru Kenyatta ayaa sheegay in Raila Odinga uu yahay Walaalkii, isla markaana ay billaabayaan geedi socodka ay wada xaajoonayaan halka ay dhibaatada iyo kala qeybsanaanto ka timid.
"Regrettably, we have responded to our challenges by mostly running away from them", said Odinga, who spoke first.
A High Court has since overruled the government's move and ordered that Miguna be allowed back into the country.
"Mr. Odinga's unilateral, irrational and erratic decision to betray the fight for electoral justice, the culture of impunity and the flagrant abuse of human rights that have become routine under the illegitimate regime of Uhuru Kenyatta and William Ruto can not be justified", he wrote.
That's not a coincidence, said independent political analyst Martin Andati.
With the country at breaking point and growing political and economic injustices reigniting deeply ethnic hatreds, Raila Odinga chose yet again a path he often has: the path of negotiation rather than confrontation to right the wrongs and protects the people from the horrors that this drawn-out, looming conflict posed.