Wickremesinghe's comment comes as Australia increases pressure on failed asylum seekers on Papua New Guinea's Manus island and the tiny island nation of Nauru to return home voluntarily, including offering large sums of money, amid fears a deal for the United States to take refugees has collapsed, REUTERS reported.
Only five men from Nepal on Manus have so far opted to leave despite the threat of deportations.
Australia does not publish details on the nationalities of the 1,152 people held on Manus and Nauru though refugee advocates said there are approximately 150 Sri Lankans detained.
Many of these would have received their refugee status, advocates said, but for those who have been rejected, they face the choice of accepting the offer of cash from Australia or the threat of deportation.
"They are welcome to return to Sri Lanka and we won't prosecute them," Wickremesinghe told reporters in Australia's capital Canberra.
Despite the assurances from Wickremesinghe, refugee advocates said many Sri Lankans would be reluctant to return home amid reports of mistreatment of members of the ethnic Tamil minority, a claim Wickremesinghe rejected.
"It is quite safe for them to come back... we want all the Tamils to come back," said Wickremesinghe.