Palestinian medical officials said about a dozen people were slightly wounded by debris from the air strikes. There were no Israeli casualties.
A Palestinian group that identifies with al Qaeda claimed responsibility for firing the rocket and mortar shells at Israel from Gaza, which is ruled by the Hamas.
Hamas security sources said the Israeli air strikes hit an airport in the southern Gaza Strip which is not in use and a Hamas training camp in the north.
An Israeli military spokesman said the air strikes were a response to the cross-border attacks from Gaza and that warplanes had targeted tunnels used by militants.
Hamas, which seized the Gaza Strip from forces loyal to Palestinian President Mahmoud Abbas in 2007, says it has reached an understanding with other groups to halt rocket fire. But smaller groups have carried on firing at Israel.
Israel says it holds Hamas responsible for any attacks carried out from the coastal territory.
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