The National Super Alliance (Nasa) is alleging massive discrepancies in the forms 34A and 34B coming from constituency and county returning officers.
ODM deputy party leader Hassan Joho said Wednesday evening after the Independent Electoral and Boundaries commission (IEBC) chairman Wafula Chebukati announced a joint verification of the forms by commission officials and party agents.
Mr Chebukati’s order was in response to claims by Nasa presidential candidate Raila Odinga that the agency's system had been hacked and that the results it had been announcing were different from those coming from the polling centres.
Forms 34A and 34B originate from the constituency and county returning officers respectively.
Mr Joho, who has successfully defended his Mombasa governorship seat, also faulted the pace of the verification, saying one laptop provided by IEBC was not adequate.
He also asked their supporters to ignore the presidential results so far released by the commission, charging that they are a product of fraud.
Mr Odinga had earlier in the day dismissed the results that are giving Jubilee presidential candidate Uhuru Kenyatta the lead as dubious.
"Tumeshinda tena kwa kura nyingi sana (We have won with a huge margin). Our parallel tallying indicates that we are ahead of Uhuru," Mr Joho said when he joined other opposition luminaries at Bomas of Kenya, the national tallying centre.
IEBC will rely on the two forms to generate another one, 34C, to help it determine if the leading presidential contender has attained the constitutional requirement of 50 per cent plus one vote.
Similarly, the National Council of Churches of Kenya (NCCK) General Secretary Peter Karanja led other religious leaders in a meeting with the commission's officials Bomas of Kenya to express their concerns regarding the issues advanced by Nasa.
Anglican Church of Kenya Archbishop Jackson ole Sapit said the results manipulation claims are weighty and need concrete answers.
"We are confident IEBC is working to address the issues," he said at Bomas on Wednesday.
The prelates further called on Kenyans to remain calm as the tallying continues.
Mr Chebukati has five more days to declare the presidential winner although he has indicated he will do so by or before Friday.
"The commission is actively engaging stakeholders to resolve the matter and we asked the parties to use the platform to raise their concerns.
"We also urge Kenyans to be peaceful as we are confident that the commission and the parties involved would resolve the concerns," Canon Karanja said.
At the same time, the Commission denied reports that it was planning to prematurely call the presidential race in favour of President Kenyatta.
"We have not announced any plans to declare the winner of the presidential election tonight. Ignore the circulating SMS," head of communication Andrew Limo said.
The development saw more anti-riot police deployed around Bomas of Kenya with additional water cannons to thwart violence.