He urged the public to help authorities by keeping vigilant while calling on the media to be careful with their coverage.
Gen Prayut said this was a sensitive matter and the wrong kind of coverage could intensify hatred and conflicts.
Gen Prayut, who is scheduled to leave today for a one-day visit to Malaysia, is expected to raise the attacks in Thailand at his meeting with his Malaysian counterpart Najib Razak.
Thawip Netniyom, National Security Council (NSC) chief, told reporters Monday it is too early to conclude whether the attacks in the seven provinces are the work of the BRN as some groups have suggested.
Meanwhile, Singapore will continue to step up security arrangements after the string of bombings in Thailand, Singapore Defence Minister Ng Eng Hen said.
The attacks demonstrated how small arms, including explosives, are easy to obtain illegally, he said.
"Our security forces and agencies have already stepped up their activities and security arrangements. But if any attack occurs, I think we have to make sure we hold together," Monday's Today newspaper quoted the minister as saying.