Ranil Wickremesinghe said the government believed Sunday's attacks could not have been carried out without help from terror groups abroad.
The first mass funeral was held on Tuesday as Sri Lanka marked an official day of mourning for the victims.
A state of emergency remains in effect to prevent further attacks.
Police have now detained 40 suspects in connection with the attack, all of whom were Sri Lankan nationals.
The Islamic State (IS) group claimed the attack on Tuesday via its Amaq news outlet. Sri Lanka's government has blamed the blasts on local Islamist group National Thowheed Jamath (NTJ).
"This could not have been done just locally," Mr Wickremesinghe said. "There had been training given and a coordination which we are not seeing earlier."
The nearly simultaneous attacks targeted three churches packed for Easter services and three major hotels in the capital, Colombo.
An attack on a fourth hotel on Sunday was foiled, Mr Wickremesinghe said. He also warned that further militants and explosives could still be "out there" following the attack.