Syrian state news agency SANA said on Saturday Syrian air defences were responding to a "new Israeli aggression".
Israel says it does not want war but will not hesitate to defend itself against any attacks or attempts by Tehran to get a foothold in Syria.
Prime Minister Benjamin Netanyahu of Israel spent much of Saturday in consultations with his defense minister, the Israeli chief of staff, and other military officials.
In the autumn of 2015, Israel and Russian Federation agreed to exchange data in order to safeguard their militaries against any accidental engagements during operations in Syria.
"My impression is that it seems to be contained at this point", a Western diplomat in the region told Reuters.
The drone entered Israeli airspace at 4:50 a.m. local time Saturday after being tracked by the Israeli military from its launch from the Iranian T-4 command center near Palmyra, Syria, Conricus said. The plane crashed Kibbutz near Harduf in the Lower Galil south of Shfaram on Shabbos.
The military called the drone infiltration a "severe and irregular violation of Israeli sovereignty" and said Iran would be held responsible for its outcome, marking a dramatic escalation in tensions along its northern border.
Air raid sirens sounded in the early morning of the Jewish sabbath in northern Israel and flights at Tel Aviv's global airport were briefly halted.
The area was quiet by mid-afternoon.
Iran strongly rejected the claim as "ridiculous", noting that such allegations do not merit a comment.
Iran on Saturday denied any role in shooting down the Israeli jet.
In September, Israel's military shot down an Iranian-made drone operated by Lebanese militant group Hezbollah on a reconnaissance mission over the Golan.
Iranian and Iran-backed Shi'ite forces, including Lebanon's Hezbollah, have deployed widely in support of Assad.
Open conflict across the Syrian border is unlikely to be in the interest of either Israel or Iran-aligned forces at the moment.
Israel has mostly stayed out of the fighting in Syria, wary of being drawn into fighting between forces that are all opposed to it.
Two F-16 pilots ejected as the plane went down in northern Israel.
"I do not believe matters will develop to a regional war", the official said.
Iran's actions have proven correct all of Israel's warnings against allowing Iran's establishment in Syria.
Netanyahu said he had spoken by telephone with Russian President Vladimir Putin and that they agreed Israel-Russia military coordination in regard to Syria would continue. They noted that this was the first time in recent years that Israel struck Syrian territory in broad daylight.