After complaining of fraud, Odinga told Reuters he believed most of more than 20,000 polling station result forms uploaded to the election commission's website were fake.
IEBC released a statement saying that the system was secure during the elections and that no results were manipulated.
Small-scale protests erupted in the slums of Nairobi and elsewhere in the country and police shot dead at least two protesters they accused of looting. Later in the day, Mr Odinga's National Super Alliance reiterated its claim that the elections had been hacked and that Mr Odinga had won with more than eight million votes.
An worldwide observer mission is urging Kenyans to be calm as they await final election results following opposition allegations of vote-rigging and the deaths of several people in election protests.
Speaking to the BBC, John Mahama, former president of Ghana and head of the Commonwealth Observer Mission in Kenya, said the responsibility to maintain calm fell to the two leading candidates.
While President Uhuru Kenyatta has an unassailable lead in near-complete provisional results, Odinga insists these are a "sham", produced by a massive hacking attack on the electronic vote tallying system.
"We demand that the IEBC [Independent Electoral and Boundaries Commission] chairperson announce the presidential election results forthwith and declare the right honorable Raila Amolo Odinga and his excellency Stephen Kalonzo Musyoka as the duly elected president and deputy president of the republic of Kenya, respectively", said Mudavadi. Some businesses were open in the city center but mostly people were remaining indoors; other residents who went to their home villages to vote might also have stayed away.
Kenyatta is the son of Jomo Kenyatta, Kenya's first president, and Odinga is the son of Jaramogi Odinga Odinga, the country's first vice president.
Meanwhile, the global observer missions present in Kenya, has called on the IEBc to undertake the tallying with full integrity and transparency so that all Kenyans could trust the announced results.
However, the protests remained isolated, and in Opposition strongholds where elections tend to stoke tensions.
"We are happy. we need peace and we need the correct results", said 35-year-old Anthony Karaba, as a police helicopter hovered overhead. "We know the consequences of what happened in 2008 and we don't want to see a repeat of that".
Wafula Chebukati, the commission chairman, centre, says the election hacking attempt failed.
"Voting and counting was assessed as very well conducted and transparent".
Finally Article 249 of the Constitution stipulates that the Commission is independent and not subject to the control of any person or authority.
Odinga has dismissed the results as a "fraud". Long queues could be seen, and video footage at one polling station showed people injured after an apparent stampede.
Kenya had been relatively calm since the election but had braced for possible violence Friday night with police in the central business district.
"IEBC must not hurry the announcement until all parties are satisfied beyond doubts with results in the spirit of fairness", added Mudavadi.