AFP correspondents saw flyers dropped over the Zeitun neighbourhood southeast of Gaza City, and residents there and elsewhere also reported receiving recorded phone and text messages asking them to evacuate by 0500 GMT .
The flyers explained that the army would be carrying out "aerial strikes against terror sites and operatives" in Zeitun and Shujaiya, since "a high volume of rocket fire at Israel" was from there.
A similar message was sent to residents of Beit Lahiya in northern Gaza.
Similar messages had been sent to Beit Lahiya with a Sunday deadline, causing the exodus of 17,000 people who took shelter in United Nations schools.
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The warnings came on the ninth day of Israel's Operation Protective Edge, which aims to stamp out rocket fire from Gaza militants.
Since July 8, militants have fired nearly 1,000 rockets and mortars into the Jewish state, and Israel has carried out around 1,500 strikes against targets inside the Gaza Strip, the army says.