The decision is reported to have been taken without consultation with key advisers, including Mr Tillerson.
He further pointed out that Raila did not consult the other three Nasa co-principals before the meeting with President Uhuru on Friday.
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.
"This is a purely domestic initiative", Mr Odinga's spokesman Dennis Onyango said.
For many observers, the historical divisions between the Kenyatta and Odinga dynasties and the ethnic groups they represent cloud the promise of Kenya's democracy. The Supreme Court earlier nullified an August presidential poll and ordered the October re-run.
"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.
In a statement posted to Facebook on Friday, he called the rapprochement "a fundamental betrayal of the innocent Kenyans who have lost their lives" supporting Odinga in several elections over the last decade.
"Time has come for us to confront our differences because they are becoming too entrenched", said Odinga.
Mr Odinga said that nothing had been changed before the re-run.
The controversial MP whose election Narok Court upheld last month added that the Kalenjin unity was of paramount importance if Ruto wishes to gun for the presidency in 2022 General election with the whole community behind him.
He said they have agreed to stop any dissent immediately and not to allow the country's diversity to kill their nation.
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.
Odinga, who spoke first, expressed similar sentiments.
On Friday morning, Mr Odinga and Mr Kenyatta met at Harambee House in Nairobi.
Senate speaker Ken Lusaka and Kiambu Senator Kimani Wamatangi speaking on the sidelines of an induction retreat for members of the senate roads committee, said the move will unite the country. "They have successfully engineered this", said Aly Khan Satchu, an independent analyst in Nairobi.
"Where is the problem of having a grand-coalition government since after all this country belongs to all of us".