(Updates with polls closing)

By Wangui Kanina and Duncan Miriri

NAIROBI, June 11 (Reuters) - Kenyans voted peacefully on Wednesday for five parliamentary seats that will decide who holds the majority, in a test of stability for a nation still recovering from a deadly post-election crisis.

It was the first voting since President Mwai Kibaki's disputed December re-election set off ethnic violence that killed at least 1,300 people and displaced 300,000 more in the east African country.

Armed police in riot gear with dogs patrolled polling stations in a reminder of the fear of a re-eruption of conflict.

"I think if the by-elections are peaceful and transparent and are generally regarded that way, that will show that Kenya has learned from the experience of December and is moving ahead democratically," U.S. Ambassador Michael Ranneberger told Reuters.

By most accounts, the polls went smoothly until they closed at around 1500 GMT, with a few polling stations staying open a few minutes extra.

"Where we had a problem, in one or two of the small stations where they started a little late, we compensated for the time. Counting is under way," Electoral Commission of Kenya (ECK) spokesman Mani Lamayan said.

Counting was expected to finish overnight, barring any problems, he said.

In the December poll, accusations of vote-rigging flew during the counting process, and the international observers roundly criticised the ECK for its handling of the polling.

Prime Minister Raila Odinga's Orange Democratic Party (ODM) and Kibaki's Party of National Unity (PNU) are each seeking to boost their numbers in parliament.

"We learnt a lot with what happened in the last election. This time I have no fear of violence. We are not thinking of tribes," said Issak Mureithi, 45, a voter in Nairobi's Embakasi constituency.

The by-elections are to fill seats where two ODM legislators were shot dead and another two constituencies that remained undeclared in the chaotic aftermath of the election.

The fifth is that of the parliamentary speaker, who resigned from his constituency after getting the speaker's chair.

Two more ODM legislators, Roads Minister Kipkalya Kones and Home Affairs Assistant Minister Lorna Laboso, died in a plane crash on Tuesday. Flags flew at half-mast on Wednesday.

No plans have yet been announced to fill their seats.

RIGGING CLAIMS

In Embakasi constituency, ODM candidate Esther Passaris accused rival PNU officials of rigging, the kind of claim that set off rioting after the December poll.

"The PNU agents in every polling station are bribing voters, in front of the ECK. This is exploiting poverty," Passaris, a former beauty queen and entrepreneur, told reporters.

PNU candidate Ferdinand Waititu denied Passaris' accusation.

Odinga and Kibaki formed a coalition government in April, with Odinga, a former political prisoner, becoming only the second prime minister of Kenya since the east African country won independence from Britain in 1963.

Odinga's party won 99 seats to 43 for Kibaki's in the December vote. But in practice it is an even split because Kibaki-allied legislators from other parties joined PNU to make up half the parliament.

Campaigns for the by-elections were marred by some violence among supporters, but nothing like the full-scale fighting earlier this year. (Editing by Bryson Hull and Andrew Roche) (For full Reuters Africa coverage and to have your say on the top issues, visit: http://africa.reuters.com/)

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