The UNP has won the most seats in 41 bodies.
Official results showed Rajapakse's Sri Lanka Podujana Peramuna - SLPP or People's Front - had won 160 of the 241 councils counted so far, out of a total of 340.
President Maithripala Sirisena, Prime Minister Ranil Wickremesinghe and former President Mahinda Rajapakse were among those who voted early on Saturday.
Police said those arrested, including eight candidates, conducted minor violations such as pasting election related posters, taking photographs of ballot papers and political party members transporting voters to polling stations.
Mr Sirisena was voted into office on the strength of support mainly from minority Tamil and Muslin communities.
At a press briefing this morning, the leader of the Joint Opposition, Dinesh Gunawardane said the unity government had "no option but to resign", arguing the mandate given to it by the 2015 election had expired yesterday. Sirisena faces a sterner challenge from his predecessor Mahinda Rajapaksa.
Sirisena's relationship with Wickremesinghe, his main supporter when he defeated Mr Rajapaksa in the presidency in 2015, has soured in recent months. Rajapaksa had backed opposition alliance which was contesting on anti-government plank.
His faction of the SLFP has been accused of delaying the election out of fear of losing them by the faction led by former president Rajapaksa.
Voting for the local government elections is the first conducted by the newly-established independent Election Commission as well as the police under the Independent Police Commission.
In order to postpone the polls by a year, the government proposed an amendment to the Constitution to hold elections for all nine provincial councils on a single day. Only MPs can through a two thirds majority in parliament seek a dissolution of the legislature and ensure a snap general election.
Another key feature of the election is the 25% quota for women council members.
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