(Updates with new statement)

BRUSSELS, Jan 3 (Reuters) - U.S. Secretary of State Condoleezza Rice and EU foreign policy chief Javier Solana urged Kenya's rival political parties to work to form a government, an EU spokeswoman said after the two spoke by phone on Thursday.

The EU said initially that Solana and Rice had agreed on the need to encourage the parties to form a coalition government, but it later clarified the statement to stress that the shape of the future government was for Kenyans alone to decide.

"They agreed the focus is on jointly encouraging the parties in Kenya to engage in dialogue and their dialogue must aim at halting the current destabilisation, stopping the violence and on setting up a government," a Solana spokeswoman said.

"It is up to the parties in Kenya to decide on the government they form. The important thing is that we are encouraging them to enter into dialogue," she added.

Over 300 Kenyans have been killed in a week of tribal and political violence triggered by the disputed re-election of President Mwai Kibaki.

U.S. President George W. Bush urged Kenyans on Thursday to refrain from further violence and called on Kenya's president and opposition leader to "come together" in an arrangement to resolve their bitter election dispute.

State Department spokesman Sean McCormack said Rice telephoned Kibaki on Thursday morning and opposition leader Raila Odinga the previous night, urging them to "broker some political solution to the political crisis".

Solana also raised with Rice the possibility of a joint EU-U.S. mission to Kenya and the two agreed to remain in close contact on the situation, Solana's spokeswoman said.

"It is possible that might be one way (to help)," she said of the mission, which if agreed could involve a joint envoy or team of envoys.

Kibaki was sworn in on Sunday after official results showed he had narrowly beaten Odinga.

However, each side has accused the other of vote-rigging and EU observers said the elections fell short of international standards.

Earlier EU statements this week noted that, despite concerns over irregularities, the vote appeared to be a very close race and called on Kibaki and Odinga to work together for an "inclusive" political solution. (Reporting by Mark John; editing by Darren Ennis and William Schomberg)

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