The decision is reported to have been taken without consultation with key advisers, including Mr Tillerson.
Lawyer Miguna Miguna has accused Nasa leader Raila Odinga of betraying Kenyans by pledging to work with President Uhuru Kenyatta.
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.
Bilowgii sanadkan, Mr. Odinga ayaa isu dhaariyey Madaxweynaha shacabka waxa uuna diiday in uu Mr. Kenyatta u aqoonsado in uu doorashada ku guuleystay oo uu Madaxwayne yahay.
The leaders said they had agreed to set up an office staffed by advisers to tackle issues ranging from opposition complaints over the election to tensions between ethnic groups and corruption.
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.
In a statement posted in his Facebook page and on his official Twitter handle, Mr Miguna said Mr Odinga's "erratic decision to betray the fight for electoral justice" can not be justified.
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.
Odinga said: "the conflict is over" and called on the country to "reconcile and move on". "We refuse to allow our diversity to kill our nation", he said.
Mr Tillerson was in the Ethiopian capital of Addis Ababa when news of Donald Trump's agreement to meet Mr Kim in unprecedented talks broke late on Thursday.
A statement signed by Kalonzo Musyoka, Musalia Mudavadi and Moses Wetangula stated that they were not part of the meeting.
He later met with President at State House where he stated the U.S. was interested in widening its investment in Kenya as well as strengthening the bilateral and trade relations between the two countries. "They have successfully engineered this", said Aly Khan Satchu, an independent analyst in Nairobi.
Waxaa ku guuleystay doorashadii ku celiska ahayd ee Kenya ka dhacday bishii October ee sanadkii 2017 Uhuru Kenyatta, taasi oo Mr. Odinga uu qaadacay.
"It's a really good step towards harmonizing the country", said Brian Wanjoki, a pedestrian.