Wickremesinghe said former president Mahinda Rajapakse had agreed to help stop boats carrying asylum-seekers leaving for Australia if Canberra kept quiet about alleged abuses by Rajapakse's regime.
In an interview with The Australian newspaper, Wickremesinghe said Australian Prime Minister Tony Abbott's close relationship with Rajapakse, who was voted out of power last month, was "a mystery" to Sri Lankans.
Colombo's new premier also said that "people connected to the previous government" had taken part in people-smuggling operations.
"You could not have got anyone out of this country without someone in the security system looking the other way, the police or the navy."
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The arrival of asylum-seekers by boat is a sensitive political issue in Australia, which in 2013 started sending those picked up on boats to offshore camps on Papua New Guinea's Manus Island and Nauru.
Wickremesinghe said he was not against the Australian government, but urged them to learn from their experiences.
"Some other countries must also, that fully backed the Rajapakse regime," he told the newspaper.
"When human rights were being trampled, and democracy was at bay, these countries were silent. That is an issue for Sri Lanka."
Sri Lanka's new government has promised a domestic probe into alleged war crimes under Rajapakse.
Ahead of travelling to Sri Lanka in 2013 for a Commonwealth summit, Abbott said he was "not inclined to go overseas and give other countries lectures" but he would be urging Colombo to "respect everyone's rights".
A spokesman for Abbott said today that relations with Sri Lanka remained strong.