The National Heritage Party (JHU) said the local council vote, in which the ruling parties were hammered, showed people were unhappy with Prime Minister Ranil Wickremesinghe.
"There must be urgent reforms," said JHU leader Champika Ranawaka, who is minister for urban development.
"There must be giant changes that will directly address the aspirations of the people."
Wickremesinghe has accepted responsibility for the defeat and said he will change the government as well as his United National Party (UNP).
Rajapakse, whose family wields enormous influence in Sri Lanka, has staged a dramatic comeback after launching his Sri Lanka Podujana Peramuna or Peoples Front party.
The ruling coalition has also been plagued by internal divisions that burst into the open in the run-up to Saturdays election.
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