The military said it was trying to hit rocket sites pre-emptively as blasts rocked different points including what witnesses described as a training camp in the northern part of the Gaza Strip and an open area in the south.
At least one man was killed and one wounded, medical officials said.
Their identities were not immediately clear.
Minutes after the strikes, sirens sounded in Israel - initially among border communities but soon also in and around the commercial capital Tel Aviv, 60km north of Gaza.
There was no immediate word of casualties in Israel, although local media reported a home was hit in the town of Sderot.
In Gaza, multiple contrails could be seen ascending as rockets were launched.
Mid-air explosions signalled interceptions by Israel's Iron Dome aerial defence system.
On Tuesday, Israel launched a series of strikes it said were aimed at senior leaders of Islamic Jihad responsible for planning attacks against Israel.
At least 10 civilians were killed in the strikes as well as three senior commanders.
"We have no intention of waiting until they launch (rockets)," Israeli security cabinet minister Avi Dichter told Kan radio after Wednesday's renewed Gaza strikes.
"If launches can be prevented or disrupted, if launch crews can be hit - all of this ultimately creates deterrence."
There was no immediate claim of responsibility for Wednesday's rockets.
Islamic Jihad had promised to retaliate for the strikes.
"The resistance decides the timing of the response in line with its tactics and calculations because we see that the response must match the size of the crime," group spokesman Dawoud Shehab said.
As many as 30 per cent of residents of Israeli border communities evacuated as a precaution, municipal head Gadi Yarkoni told Kan radio.
Earlier on Wednesday, Israeli forces killed two Palestinians who opened fire on them in Qabatiya, in the occupied West Bank.
Islamic Jihad claimed the two as members.
The army said the two Palestinians fired on troops from a car and were shot dead.
An assault rifle was recovered from the vehicle, it said, adding that there were no Israeli casualties.
In Gaza, businesses and schools remained closed.
Israel kept its two commercial and people crossings with Gaza closed.
The move would stop the entry of goods, fuel and humanitarian aid as well as patients, who receive treatment in hospitals in the West Bank and Israel.
