The Coalition for Reforms and Democracy (Cord) has demanded a stop to the vote tallying saying its integrity is "in question".
Kalonzo Msuyoka, who is the running mate of Raila Odinga, said the Independent Electoral and Boundaries Commission (IEBC) should take the blame for the flawed vote count.
"We as a coalition take the position that the national vote tallying process lacks integrity and has to be stopped and restarted using primary documents from the polling stations," said Mr Musyoka.
He, however, told supporters to remain calm.
"This is not a call to mass action."
Mr Musyoka said Cord is considering its options including moving to court to get an injunction to stop the process.
He claimed that in some cases, the total votes cast "exceeds the number of registered voters". Mr Musyoka claimed this was the case in Bureti, Kajiado south, Runyenjes, Wajir North and Kathiani constituencies.
However, IEBC figures painted a different picture. For instance, in Kajiado South, the registered voters are 46,388. The total number of votes cast are 42,276. The registered voter figure is, however, not updated on the IEBC's website and stands at 41,040.
In Runyenjes, the total votes cast are 58,395 while the number of registered voters stands at 66,410. The
registered voter figure on the IEBC website is 66,261
With votes from 108 out of 291 constituencies counted, Uhuru Kenyatta has 2,475,700 against Mr Odinga's 1,928,627.