Bush wants Rice to demand an immediate end to fighting in the East African nation.
Independent observers also found flaws in the vote count.
The result fomented tribal rivalries as well as simmering resentment over land issues and wealth disparities.
At the request of the African Union, Annan arrived in Nairobi on January 22 and launched a mediation to end violence that saw many Kenyans being hacked to death by machete-wielding mobs, burnt in churches where they had sought refuge and driven off their land.
Annan has been seeking a power-sharing deal to create a government that would pave the way for fresh elections, possibly in two years.
He said on Friday that the rival parties had agreed to a broad reform agenda to review the constitution, improve electoral laws, bolster human rights, among other measures, to “address the root causes of the crisis”.
Annan said “the only outstanding issue” remained the make-up of a coalition government.
How can Kenya resolve the crisis over the elections?
The negotiating parties are scheduled to meet their leaders before they sit down with Annan on Tuesday.
The two sides have agreed to set up an independent review commission no later than March 15 that would investigate “all aspects” of the disputed elections and produce a report in three to six months, Annan said.
He said he “will stay as long as it takes to get the process at an irreversible point”, and that this would be achieved when “a new government is established”.
During two days of talks at a secluded safari lodge in southern Kenya, Kibaki’s camp agreed to allow opposition members into government but only under the strong executive leadership of the president, according to a government official.
The opposition has pushed for the appointment of Odinga as prime minister with full powers as head of government, a post that would require changes to the constitution.
The rival leaders have been under international pressure to make concessions, with the US and UK threatening visa bans, freezing assets and other sanctions.
Condoleezza Rice, the US secretary of state, is due in Nairobi on Monday to meet the Kenya leaders and support Annan’s mediation.
George Bush, the US president, announced on the eve of a five-nation Africa tour that he had asked Rice to travel to Kenya – which is not on his own itinerary – to deliver a strong message.
Mohammed Adow, Al Jazeera’s correspondent in Nairobi, said Annan highlighted the need for consitutional reforms, parliamentary reforms, reforms in the security services, and numerous other reforms.
Adow said that with the arrival of Rice, many believe that it is international pressure that has moved this process along.