The opposition has published its own figures, putting Mr Odinga ahead of incumbent President Uhuru Kenyatta.
This contrasts with provisional electronic results giving Mr Kenyatta a clear lead in Tuesday's poll.
According to BBC, electoral commission chairman Wafula Chebukati said it was the only body legally allowed to count votes.
He accused the opposition coalition of basic mathematical errors.
International observers have described the election as free and fair.
However, many fear a repeat of the violence after the disputed election 10 years ago when more than 1,100 Kenyans died and 600,000 were displaced.