Israel's Air Force and Navy intercepted over 100 drones fired by Iran so far, with no reports of any that fell in Israeli territory, the military added.
The identity of the two suspects, as well as further details into the investigation, are under an active gag order.
Israel had prepared for the possibility that the war could last for weeks, but that timeline may now be shortened.
Meanwhile, Trump wrote on social media that Israel and Iran should and will make a deal soon and called to make the Middle East great again.
Israelis on social media reported hearing explosions, particularly in the Tel Aviv and Haifa areas.
Christodoulides said Iran had asked Cyprus to convey 'some messages' to Israel but he did not say who specifically the messages were from or what they said.
Israel conveyed a message in the last 24 hours to Iran that it would strike strategic infrastructure across the country if the Islamic Republic targets civilian population centers.
He warned that proximity to the buildings endangered their lives.
Israel also targets the headquarters of Iran's Defense Ministry • Defense Minister Israel Katz: "Tehran is ablaze"
Israel has taken a substantial bite out of Tehran's nuclear program, but it is far from down for the count.
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