The parliament's clerk announced that Marende, supported by the opposition leader Raila Odinga had won 105 votes.
The candidate supported by Kibaki's Party of National Unity (PNU) and its allies, Francis ole Kaparo, received 101 votes.
The announcement was greeted by loud cheers from opposition members, who had walked into parliament sporting orange handkerchiefs tucked in their suit pockets, in protest at what they say was Kibaki's fraudulent re-election.
The session was the first time that politicians from the government and supporters of Raila Odinga, the ODM leader, had met in public since the presidential election on December 27."We are under duty to uphold democracy," Marende said in an inaugural speech that made no direct reference to the dispute over Kibaki's re-election.
Roads were closed and riot police ringed the building as Kibaki and opposition leader Raila Odinga entered parliament at the same time, without looking at each other.
The ODM says the election, won by Kibaki, was rigged and political violence following the vote has left more than 700 people dead.
The new speaker, a 52-year-old lawyer based in the port city of Mombasa, also expressed hope "that this house will endeavour to grant Kenyans a new constitutional order at the earliest".
The speaker is a key position given that he can control the parliamentary agenda.
The ODM occupies 99 of the new parliament’s 222 seats, after many of Kibaki's former ministers and supporters were voted out in parliamentary elections held along side the presidential vote last month.
The PNU won only 43 seats but it will try to win sufficient support from other parties to overcome any obstruction by the ODM.
However the vote on Tuesday means the opposition has the initiative for now.
According to the Kenyan constitution, the presence of Odinga's MPs-elect in an assembly session convened by Kikabi could be tantamount to a recognition of the president, something the opposition has so far refused to do.
Hopes of a breakthrough in the political impasse took a firther setback when it was announced that Kofi Annan, the former UN secretary-general had delayed his trip to Nairobi after he was taken ill with severe flu at Geneva airport.
Annan had been expected to arrive in the Kenyan capital Nairobi to lead a panel of senior African political figures in the latest attempt to resolve the political crisis in Kenya.
"On his way to the airport in Geneva this morning, former United Nations secretary general Kofi Annan was taken ill with a severe flu,” the UN said in a statement from Geneva on Tuesday.
"On advice of doctors he has postponed his mission to Nairobi for a few days."
Annan's mediation comes after the US and African Union last week failed to bring Kibaki and Odinga together for talks.
The foreign affairs ministry welcomed the visit, saying it was meant "to facilitate dialogue between political leaders in the search for a lasting solution".
However, the statement contradicted comments on Monday by John Michuki, the public works minister and a member of Kibaki's inner circle, who said there was no need for international mediation.
He said: "We won the elections so we do not see the point for anyone coming to mediate power-sharing."
The violence between members of Kibaki's Kikuyu tribe and Odinga's Luo tribe have left more than 700 people dead across the country and more than a quarter of a million people have been displaced.
|Security was tight for the key parliamentary session [Reuters]|