Israel's unilateral decision to impose a "no-go zone" in the far north of the Palestinian territory comes as part of a concerted drive to thwart repeated militant rocket attacks launched from northern Gaza into southern Israel.
An Israeli army spokeswoman confirmed troops had opened fire in open fields in the "no-go zone" after a missile was fired from the area shortly before the 1600 GMT deadline came into effect.
"It's in direct response to that," said the spokeswoman, describing the artillery fire as "slightly larger scale" than previous bouts of firing.
A Palestinian militant, aged 25, was lightly wounded in the evening by
Israeli shelling as he was preparing to fire a rocket from the security zone and was taken to a nearby hospital, medical sources said.
Leaflet airdrop
The Israeli military earlier airdropped leaflets over Gaza, written in Arabic, with an accompanying map indicating the extent of the zone warning Palestinians to keep out of the area or else endanger their lives.
The confines of the security area mainly incorporate an uninhabited area where three Jewish settlements stood, before Israel withdrew all soldiers and settlers from the Gaza Strip in September after a 38-year occupation.
"The army is prepared to wage intensive operations in the north of the Gaza Strip against terrorist elements who fire rockets into the territory of the state of Israel," the leaflets warned.
"For your security you are warned to avoid the sectors indicated on the map from 6:00 pm (1600 GMT) December 28 until further notice. Those who disregard this warning will put their lives in danger," they added.
Defence Minister Shaul Mofaz ordered the application from late Monday of a decision to create the zone, taken by Prime Minister Ariel Sharon.
Palestinian leader Mahmud Abbas said Israel had no right to reassert control over any part of the territory, while also condemning the rocket strikes.
"Israel left the Gaza Strip and has no right to return under any pretext such as the firing of missiles which I also strongly condemn," he said.
"I ask all parties to assume their responsibilities and not give pretexts to Israel."
Air strikes
Alongside overnight strikes on Gaza, Israeli warplanes targeted Palestinian militants near Beirut in response to a series of rocket attacks against a town in northern Israel from across the border with Lebanon.
While there were no reported casualties in Gaza, at least two members of the PFLP-GC, a small pro-Syrian faction, were wounded in the air strike to the south of Lebanon's capital.
Palestinian security sources said the air strikes had targeted roads around the northern towns of Beit Hanun and Beit Lahiya.
The army said it had attacked 10 roads used by militants to reach rocket launch sites on the edge of the border into southern Israel.
Israeli commentators said Palestinian factions in Lebanon had been emboldened by what they regarded as a timid response to the Gaza rockets.
"He who agrees to hold back when Qassam rockets are fired in the south, will in the end endure Katyusha rockets in the north," said Yuval Steinitz, chairman of parliament's foreign affairs and defence committee.
Israeli security sources said at least three rockets were fired from Lebanon at the northern town of Kiryat Shmona, hitting the roofs of two houses.
Electricity supplies were also cut in the attacks as locals were ordered to take cover in bomb shelters. Several people were treated for shock but no one was wounded.
Military sources said it was the first time Kiryat Shmona, around eight
kilometres (five miles) south of the Lebanese border, had been hit since Israeli troops withdrew from southern Lebanon more than five years ago.
Lebanese police said a total of seven rockets had been fired from the border region. There was no immediate claim of responsibility from the Lebanon-based Palestinian factions.
"Israel wants to blame us for the rocket attacks to provoke a hostile reaction against us in Lebanon," said Popular Front for the Liberation of Palestine-General Command (PFLP-GC) spokesman Anwar Raja.
Israeli aircraft continued to overfly much of Lebanon on Wednesday,
Lebanese police said.
Britons kidnapped
Meanwhile three members of a British family have become the latest foreigners to be kidnapped in Gaza after being abducted near the Egyptian border.
Witnesses said a group of gunmen snatched a woman, her father and mother, and bundled them into a white Mercedes near the border with Egypt.
A spokesman for the British consulate in east Jerusalem confirmed the kidnappings but without releasing the trio's identities.
However a spokesman for a group called the Al-Mazen human rights centre named the daughter as Kate Burton, 24, from Scotland, saying she worked for them.
Local security sources said that it was understood that the kidnappers belonged to a group known as the Black Panthers, an armed offshoot of the mainstream Fatah movement.
The security sources said they were searching the area for the gunmen and the trio, the latest in a line of foreigners to be kidnapped in the Gaza Strip.
More than a dozen foreigners, mostly journalists and aid workers, have been abducted in the lawless Palestinian territory this year.