Loucas Louca said "cooperation and information" from foreign agencies had resulted in last week's arrest. He declined to identify the agencies involved.
"Let's leave the case to run its course, allow investigators to finish their job and we'll see where we'll conclude," he told reporters.
Police said the 24-year-old man remains in custody after his arrest in the coastal town of Limassol, and is being investigated on charges relating to national security and terrorism.
State CyBC radio has reported the suspect is a Swedish passport holder of Lebanese origin, and that documents and photographs were found in his possession detailing movements of Israelis on the island.
Police have not identified the suspect, his role in the possible attack, or the intended target.
Israeli Prime Minister Benjamin Netanyahu on Saturday blamed Iran for the alleged plot, but offered no proof to support his allegations.
"After Iran sent its people to assassinate the Saudi Ambassador on U.S. soil at the Saudi Embassy, and carry out attacks in Azerbaijan, Tbilisi, New Delhi and Africa, now it has been exposed that it intended to commit a terror attack on Cyprus soil," he said in a statement.
"The international community must fight against the biggest exporter of terror in the world."
Israeli officials could not be reached for comment.
Israel and Iran are bitter enemies. Israel considers Iran a threat to its existence because of its nuclear and missile development programs, frequent reference to Israel's destruction by Iranian leaders and Iran's support of violent groups in Lebanon and Gaza.