People gather outside the Israeli consulate during a protest to show solidarity with Palestinians, in Istanbul, Turkey, Wednesday, Oct. 18, 2023. AP
"It's a temporary measure, which should be for the short term," said the source, who refused to be quoted by name.
Israel's National Security Council late on Tuesday called on all Israelis in Turkey to leave "as soon as possible".
On Wednesday, its consulate in Istanbul said it was for their own safety given the growing "terrorist threats" against Israelis abroad. The alert level had been raised to four, the highest level, a consular spokesperson told AFP.
On Tuesday night, following a deadly strike on a hospital in the Gaza Strip, protesters demonstrated outside the Istanbul consulate and the embassy in Ankara. Dozens were hurt in clashes between police and protesters outside the consulate.
While Israel and the Palestinians have accused each other over the disaster, Turkish President Recep Tayyip Erdogan joined many Arab countries in blaming Israel, straining diplomatic relations.