Nairobi was mostly calm on Wednesday with no sign of large crowds gathering by midday, though police fired tear gas and bullets to disperse hundreds of young men in the Kibera and Mathare slums.
A protester was shot dead in Kisumu, witnesses said.
Attempts to defuse the political tension and broker talks between Odinga and President Mwai Kibaki failed to make much progress last week, prompting the opposition to call for the three-day protest, raising fears of another wave of violence that has already killed hundreds.
Previous protests, sparked by last month's election, quickly descended into tribal violence, mainly in ethnically tense western Kenya and Nairobi's slums, claiming at least 700 lives and displacing some 260,000 people in the east African nation.
Political stalemate
Odinga and his Orange Democratic Movement (ODM), who insist that Kibaki stole his way to re-election in the December 27 vote, has demanded he concede defeat to pave the way for talks.
While consolidating his hold on power, Kibaki has called for dialogue but ruled out foreign mediation, while his hardline henchmen have told the ODM to shut up or take their complaints to court.
Meanwhile, in a further blow to efforts to end the political deadlock, Kofi Annan, the former UN chief, postponed a mission to mediate the crisis "for a few days" after having taken ill with severe flu, the United Nations said in Geneva on Tuesday.
The government has refused any foreign mediation saying there is no crisis, while the opposition insists it would consider talks if there was an international middleman.
On Tuesday, the opposition candidate Kenneth Marende won the influential speaker post, dealing the government its first defeat, following hours of raucous debate.
The ODM has 99 seats in the newly elected parliament, making it the largest single party but short of an overall majority. Kibaki's Party of National Unity (PNU) won 43 seats and an ally secured 16.