William Ruto, an ODM member, said: "We are determined to ensure that Kenyans get what they deserve and that is justice attained during the polling."
"We went through elections with a secret ballot, and you stole the vote," said William Ruto, of the opposition Orange Democratic Movement (ODM), which says it was robbed of victory in a rigged presidential ballot on December 27.
Government legislators called for calm, saying rowdy behaviour dishonoured those who were killed in December's violence.
"This is the 10th election of a speaker. It has always been by secret ballot," Martha Karua, the justice minister, told the house.
"Some people with the title 'Honourable' in this House are planning murder and instituting murder," he said.
Al Jazeera's Andrew Simmons, reporting from Nairobi, said: "It's going to be a very long day ... the ODM think something suspicious is going on."
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.
It was the first time they had been in the same room since the election.
In the 222-seat parliament, ODM holds 99 seats - the highest number after many of Kibaki's former ministers and supporters were removed from power in the election.
The party hopes to elect its candidate Kenneth Marende as speaker.
Kibaki's Party of National Unity (PNU) won 43 seats but it believes it can win enough support from other parties to control the lawmaking body and overcome ODM obstruction.
There are four candidates for the post with the government side supporting the re-election of Francis ole Kaparo, a veteran speaker.
The parliament sitting began a new period of high tension after a lull in the crisis, with ODM planning to stage a wave of banned street demonstrations from Wednesday.
Tight security had been imposed in the capital Nairobi on Tuesday for the first day of parliament.
Kofi Annan, the former UN secretary-general, is due to arrive later on Tuesday to take over efforts to mediate a resolution to the post-election violence, which has left at least 700 people dead and displaced a quarter of a million.