Sin Chanpeourozet, a young female CNRP activist, was one of seven opposition councilors elected in the commune.
It went on to threaten legal action against the CNRP for “slander or false statement”.
Analysts said the comments were an attempt to gain support ahead of a general election next year.
Phouk Prathna, 25, is one of the youngest local councilors elected to run a local authority in Bavet commune, Svay Rieng province.
The Situation Room, a group comprising several election monitoring NGOs, said the CPP had spent some $15,000 on average campaigning in each commune.
The National Election Committee (NEC) said the CPP had secured 1,156 seats out of a possible 1,646 and more than 3.5 million votes.
Final results confirm dominance of Prime Minister Hun Sen's ruling party, but strong showing by opposition saw its prospects boosted for next year's general election.
The result will be announced at 9am and again at 7pm, according to the NEC’s website.
Pich Sros did not explain which law he is alleging Kem Sokha broke in what is often considered a normal part of campaigning in a democracy.
The official results of the election will be announced by the National Election Committee towards the end of the month.
Sebastian Strangio, a former reporter at the Phnom Penh Post, said the CPP felt threatened by increasing support for the opposition.
Hun Sen, Cambodia's longtime ruler, warned opposition parties not to challenge the result of June 4th local elections or they could be dissolved.
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