"The government is going to operate according to the constitution of Kenya," Mutua said.
Raila Odinga, the opposition challenger, has rejected the results of the December 27 poll, arguing they were rigged to re-elect the incumbent.
But Odinga has repeatedly said he refuses to turn to the courts, arguing that the judiciary is controlled by judges appointed by Kibaki.
Archbishop Desmond Tutu, the South African Nobel peace laureate, held talks on Thursday with Odinga, and with Kibaki on Friday, about possible coalition rule.
"There is a great deal of hope since both the Orange Democratic Movement and government have indicated they are open to negotiations," he said.
"The president was not averse to the formation of coalitions - but clearly there has to be an acceptance that there is a governing authority in the country."
Jendayi Frazer, the US assistant secretary of state for African affairs, will attempt to broker a peace on Saturday.
The US and Europe have pushed for Kibaki and Odinga to work together to bring calm in the wake of their political dispute, but said a "made-in-Kenya solution" is needed to end the violence that has killed more than 300 people and displaced tens of thousands.
The upheaval has spread from the capital to the coast and the western highlands of the country.
In Mombasa, a city heavily dependent on tourism, police scattered 1,500 protesters who were shouting "Kibaki has stolen our vote!" and "No Raila no peace!"
There were no immediate reports of injuries.
On Friday, the UN's World Food Programme (WFP) said that about 100,000 displaced people in Kenya's northern Rift Valley face starvation after the eruption of violence in the past few days.
The organisation said that it planned to start distributing food through the Red Cross soon.
| The UN says at least 250,000 people are|
internally displaced due to violence [AFP]
Andrew Simmons, Al Jazeera's Africa bureau chief, said: "It's a double-edged sword since the people who are displaced are often in far away, remote areas and difficult to access because of the security situation.
"And the humanitarian aid workers themselves have security issues because they have to evaluate the safety of travel.
"Add to that the supply line. It is cut. So, many lorries are stuck in Mombasa ... they're not moving.
"So unless this crisis cools down, there could be large regional implications for it," he reported.
Displaced in need
Nicholas Wafuna from World Vision said the situation was critical with reports of up to half a million people having been displaced.
"These people need food, they need water, they need shelter material and blankets," he told Al Jazeera.
Most of these internally displaced people are women and children, we need to protect their rights, we all have a responsibility to do that."
Many Kenyans say they have had enough of the ethnic tensions and violence in the country.
"We're tired, we're not going to march," said Samuel Muhati, a resident of the Mathare slum, where thousands of demonstrators battled police on Thursday.
"Let the fighting stop," he said.
One radio station, Kiss FM, even took the step of banning politicians from the air on Friday saying that the comments from political leaders were increasing tensions rather than defusing them.