Palestinian witnesses early on Tuesday said one missile hit an unknown target in Gaza City and another crashed into an office belonging to the Fatah faction in northern Gaza. The third hit an empty field, they said.
There were no reports of casualties.
The Israeli army said it fired two missiles at buildings used by the al-Aqsa Martyrs Brigades, a militia within Fatah faction. The buildings were used to recruit members and to host meetings by leaders of the armed group.
Israel has said it will intensify air strikes in the Gaza Strip to enforce a buffer zone to stop Palestinians from firing rockets into Israel.
The decision was taken several days ago, but bad weather in recent days had limited activity by the Israeli air force.
Palestinians reported that warplanes and helicopter gunships took to the skies over Gaza early on Tuesday and were breaking the sound barrier.
Hours earlier, fighters fired two rockets into Israel. Both hit near Israeli farming communities, with one landing next to a kindergarten. Nobody was hurt in the strikes.
The makeshift missiles rarely cause casualties but could have big political fallout as Ariel Sharon, Israel's prime minister, campaigns for re-election on the strength of a Gaza pullout that he said would boost Israel's security.
Rocket fire has not stopped despite Israel's withdrawal from Gaza in September after a 38-year occupation. Palestinian groups say the rocket fire avenges Israeli raids in the occupied West Bank and strikes into the Gaza Strip.