Turmoil since the presidential and parliamentary elections has killed at least 612 people, dismayed foreign donors, jeopardised Kenya's democratic credentials and hurt one of Africa's brightest economies.
Western powers, and Kenya's east African neighbours, have complained of irregularities in the presidential vote count.
In the toughest action from the West since the crisis began, the European Union threatened late on Monday to cut aid.
"INTEGRITY AND SOBRIETY"
Kibaki's Party of National Unity (PNU) won 43 seats in the parliamentary election. But it believes it can garner enough support from other parties to control the law-making body.
Kibaki, 76, and Odinga, 63 - a one-time member of his cabinet and former political prisoner - were facing each for the first time since the vote as parliament was sworn in.
Diplomatic efforts to get Kibaki and Odinga to negotiate appeared to suffer a blow on Monday when a senior minister and close Kibaki ally rejected Annan's mission.
"He's not coming at our invitation," said Roads and Public Works Minister John Michuki. "We won an election. We don't have a problem to be solved here."
But the Foreign Ministry, in a statement on Tuesday, welcomed the Annan mission "to facilitate dialogue".
Though the presidential vote was widely perceived to be flawed, the parliamentary ballot was given a relatively clean bill of health by most independent observers.
After parliament's opening, the opposition plans three days of nationwide anti-Kibaki protests from midday on Wednesday.
Police have banned the rallies and many expatriates are leaving Kenya in anticipation of trouble. The United Nations' 4,000 staff in Nairobi were on a Phase 2 alert - of three levels - meaning only essential staff were at desks.
In Nairobi's Mathare slum on Tuesday, crowds shouted "No Raila, no peace!" and taunted policemen on patrol. Some shouted "kesho", tomorrow in Swahili, in reference to the rallies.
Around 250,000 Kenyans are still living as refugees from the violence - an irony in a nation long used to receiving the homeless from neighbouring hot-spots like Somalia and Sudan.
