(Adds background on make-up of parliament)

NAIROBI, Jan 2 (Reuters) - Kenyan President Mwai Kibaki on Wednesday invited all members of the new opposition-dominated parliament to a meeting at State House in Nairobi, in an apparent attempt to soothe post-election tempers.

The presidential press service said in a statement that the meeting would be at 3 p.m. (1200 GMT), but it was not immediately clear how many parliamentarians would attend.

The opposition had no immediate comment.

Kibaki's Party of National Unity (PNU) saw 20 ministers lose their parliamentary seats. It won just over a third as many seats as Raila Odinga's Orange Democratic Movement (ODM), which came in with nearly 100.

Even with allied parties that will roughly double his voting power, Kibaki will still face an opposition-led parliament.

Nonetheless, Kenya's president still has a number of constitutional powers to coerce and coax legislators, including the power to appoint opposition members to his cabinet.

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