(Updates with Kibaki oath, protest details)

By Daniel Wallis and Wangui Kanina

NAIROBI, Dec 30 (Reuters) - Kenya's President Mwai Kibaki won a second five-year term on Sunday in a disputed election victory that triggered deadly riots by tens of thousands of opposition supporters.

As smoke billowed from protests in Nairobi slums, Kibaki was sworn in on the lawn of State House just an hour after the result was announced, his hand on a Bible. Opposition supporters accused the government of vote rigging.

The 76-year-old Kibaki urged Kenyans to put aside election "passions" and promised a corruption-free government to forge unity in the polarised east African nation of 36 million, long seen as an island of relative stability in a volatile region.

"I thank all of you for the trust you have bestowed upon me," he said. "I urge all or us to set aside the passions that were excited by the election process and work together."

Some Kibaki supporters celebrated in the streets.

But they were quickly outnumbered by furious supporters of opposition rival Raila Odinga.

Local TV said 10 people were killed in Kisii, in Odinga's ethnic Luo homeland. Police shot into a crowd in Kisumu, killing another three people, residents and witnesses said. A Reuters reporter was attacked in Kisumu.

Odinga has accused the government of widespread rigging -- allegations that had already fuelled two days of ethnic riots.

In Kibera, Nairobi's biggest shantytown, witnesses said protesters burned shacks as they chanted pro-Odinga slogans.

"There's a lot of heat over here. People are out in their thousands," Kibera resident Joshua Odutu said against a backdrop of gunshots, whistles and shouting.

The head of Kenya's electoral commission (ECK), Samuel Kivuitu, declared Kibaki winner amid chaotic scenes at the main vote tallying centre. Kivuitu had to be escorted to safety by paramilitary police.

"DOUBT REMAINS"

Chief European Union observer Alexander Graf Lambsdorff said some doubts remained about the accuracy of the final count.

"We believe that, at this time, the ECK, despite the best efforts of its chairman, has not succeeded in establishing the credibility of the tallying process to the satisfaction of all parties and candidates," he said in a statement.

"We regret that it has not been possible to address irregularities about which both the EU (observer mission) and the ECK have evidence... some doubt remains as to the accuracy of the result of the presidential election as announced today."

Odinga's officials were locked in a crisis meeting after the announcement and did not immediately comment.

Delays announcing official results have triggered furious protests and ethnic clashes across Kenya.

The few supermarkets and food shops that opened were packed with nervous customers earlier in the day. Shelves of meat, milk, beer, bottled water and other provisions emptied fast.

Business leaders said this weekend's tribal clashes were costing more than $30 million a day in lost taxes -- not to mention looting damage -- and threatened investment in Kenya.

One election observer who asked not to be named said they were "in very little doubt" there had been rigging. (Additional reporting by Guled Mohamed in Kisumu, Katie Nguyen, Nicolo Gnecchi, Helen Nyambura-Mwaura, Duncan Miriri, Bryson Hull, Andrew Cawthorne, George Obulutsa and Tim Cocks; Editing by Matthew Tostevin)

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