KIEV — Nearly a week after Ukraine’s parliamentary election, officials on Friday were still counting votes in eight key districts across the country, in what the opposition says was a clear example of widespread vote-rigging by the ruling ­party.

The disorderly count has touched off Ukraine’s penchant for violent political passions. As the count dragged on at one election commission in the capital, fistfights broke out, tear gas was fired, and an election official broke down in sobs. At another election commission in Kiev, police pushed the opposition candidate when he tried to approach a table where ballots were located and he broke a rib and finger when he fell.