Kufuor, Ghana's president, met President Mwai Kibaki first at State House before holding talks with Raila Odinga at a central hotel. He then returned to Kibaki and was due to speak to Odinga again on Thursday.
Kibaki's office said the president and Kufuor reiterated that dialogue was "the only way forward towards a sustainable solution to the current political situation."
An opposition spokesman said Odinga discussed forming a transitional government, a vote recount and a new poll as possible options to end a crisis that has dented Kenya's reputation for stability in volatile east Africa.
"(Kufuor) will leave very soon, after having created a framework in which these negotiations can take place," he said.
Odinga says Kibaki supporters cheated him out of the December 27 vote by rigging. Washington and London have said the vote counting was flawed.
Previously regarded as a gentlemanly leader with a passion for golf, Kibaki has revealed a steely side.
He announced the core of a new cabinet on Tuesday that ignored Odinga's party and triggered a night of riots in the western opposition stronghold, Kisumu.
Washington said the U.S. envoy in Kenya, Jendayi Frazer, spoke to Kibaki about the move.
"The perception was he was trying to put in place a political fait accompli." U.S. State Department spokesman Sean McCormack told reporters. "We expressed our displeasure, we were quite disappointed by the action."
Kibaki told Frazer the step was intended only to keep the government running while there was a negotiated political settlement to the crisis, McCormack said.
Kenya's main Daily Nation paper said the appointment of 17 ministers on Tuesday - including several figures hated by the opposition - might "poison the atmosphere" further.
"It will be seen as a sign of bad faith ahead of the discussions about to begin," the newspaper said.
Kibaki has implied he could bring opposition figures into government and invited Odinga to a face-to-face meeting on Friday. But Kibaki's former ally has declined, saying such a meeting would be a "sideshow" without an international mediator.
The violence has already uprooted more than a quarter of a million people in Kenya, which is more used to hosting refugees from hot-spots such as Sudan and Somalia.
In New York, U.N. humanitarian chief John Holmes said he had approved a first allocation of $7 million (3.5 million pounds) from the U.N. central emergency response fund to help agencies and aid groups working in Kenya. "I'll be prepared to look at further applications ... if the crisis continues," he told reporters.
In his first public foray on Wednesday, Kibaki's office said the president called on Kenyans to respect the election result - indicating limited room for manoeuvre.
Kibaki vowed to punish politicians accused of inciting attacks during a visit to the Burnt Forest area, near Eldoret in west Kenya, one of the areas worst hit by ethnic killings.
Speaking on a hastily erected wooden stage draped in Kenya's national flag, the 76-year-old leader also promised aid to rebuild homes to a crowd of several thousand displaced people.
"We will have peace. This is your country and no-one can take it from you," he said, urging the crowd not to fear "backward, savage people."
Officials say 486 people have died in election-related clashes between police and protesters, ethnic fighting, and looting. But aid workers put the figure at more than 500, and the opposition say the toll could be nearer 1,000.
International pressure for a negotiated solution is growing.
But, there is deep distrust between Kibaki and Odinga, a former political prisoner and wealthy business owner who helped Kibaki win a 2002 poll but was sacked from government in 2005.