(Adds comment from Obama, more from McCormack)

By Sue Pleming

WASHINGTON, Jan 8 (Reuters) - The United States on Tuesday pressed Kenya's opposition and government to hold talks to end a political crisis as the top U.S. diplomat for Africa extended a visit to the East African nation to help reconcile the two.

"We think that it is of primary importance that they open up those channels of communication," State Department spokesman Sean McCormack said.

"They need to agree upon something that they can both live with that ends the political crisis and therefore ends the possibility of any further political violence," he added.

But Kenyan opposition leader Raila Odinga on Tuesday rejected a government offer of bilateral talks to end a crisis that has killed at least 500 people and displaced some 255,000, saying that without international mediation such a meeting would be a sideshow.

Shunning international pressure, Kenyan President Mwai Kibaki and Odinga have still not met since violence erupted after Kibaki's disputed re-election last month.

Kibaki, who sees the crisis as a domestic issue, has been reluctant to accept international mediation despite the constant prodding of the United States and others.

On Tuesday, protests erupted after Kibaki named several members of a new cabinet, a political gesture that McCormack said was disappointing.

"There's been really just a sad amount of loss of life here -- needless loss of life. And these two leaders need to come together to find a way to bridge the differences," he said.

The State Department's top diplomat for Africa, Jendayi Frazer, had planned to leave Nairobi on Tuesday after several days of trying to mediate but McCormack said Secretary of State Condoleezza Rice had asked her to extend her trip.

He said Frazer would make a one-day, pre-scheduled trip to the Comoros on Wednesday but immediately go back to Kenya.

OBAMA CALL

In a further diplomatic push to end the crisis, African Union chairman, Ghanaian President John Kufuor, was in Kenya on Tuesday to meet Odinga and Kibaki, and McCormack said Frazer also planned to consult the AU leader on how best to proceed.

Frazer has been harshly critical of Kenya's political leaders following the election and the violence that ensued, saying earlier this week that Kenyans had been "cheated by their leadership and their institutions."

Odinga says his rival Kibaki stole the Dec. 27 election and must step down and make way for a new vote after a transitional period.

U.S. pressure to end the crisis is also coming from politicians such as Sen. Barack Obama, a Democratic hopeful for the White House, who called Odinga on Monday and said he also plans to speak to Kibaki.

Obama, whose father was Kenyan and came from the same Luo tribe as Odinga, said Odinga indicated he would be prepared to meet with Kibaki, who is from the Kikuyu tribe.

"What I urged was that all the leaders there, regardless of their position on the election, tell their supporters to stand down, desist with the violence and to resolve this in a peaceful way in accordance with Kenyan law," Obama said during a campaign stop in Manchester, New Hampshire.

"He (Odinga) gave me some encouraging signs that he would be willing to have such a meeting," added Obama, who belongs to the powerful Senate Foreign Relations Committee. (Additional reporting by Mark Egan, Editing by Eric Walsh)

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