AFP correspondents saw dozens of rockets fired from north and east of Gaza City, while the Israeli army confirmed in a statement that warning sirens had sounded in towns bordering the strip, including Sderot and Ashkelon.
Earlier, the Tel Aviv municipality had decided to open public shelters in anticipation of rocket fire from the Gaza Strip.
Since dawn on Tuesday, powerful explosions rocked Gaza and video footage on social media showed billowing smoke and flames lighting up the night sky.
The airstrikes represent the latest chapter in the escalation of violence for more than a year, as Israeli military raids are repeated and settler violence intensifies in the occupied West Bank.
More than 90 Palestinians and at least 19 Israelis have been killed since January.
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