At least two Palestinians have been killed in an Israeli air strike on two cars in the eastern part of Gaza City.
Israel's defence minister said militants should expect a response
The Israeli army confirmed it had carried out the strike, the latest in a series launched in response to rocket attacks on the Israeli town of Sderot.
The two men killed were identified as members of the militant group Hamas.
The raids, which began before dawn on Saturday, are Israel's first in the Gaza Strip since its military withdrawal almost two weeks ago.
In the early hours of Saturday, militants fired 30 rockets into the town of Sderot, wounding five Israelis.
Hamas said the rocket attacks were themselves a response to an explosion at a Hamas rally on Friday afternoon, which killed at least 15 people.
Israel denies it was responsible and the Palestinian Authority said it appeared to have been an accident caused by Hamas members carrying explosives in an area packed with people.
Israel's defence minister promised a "crushing response", and ordered the West Bank and Gaza borders sealed.
"We have to make it clear to the Palestinians that Israel will not let the recent events pass without a response," Shaul Mofaz said in a statement.
"The response needs to be crushing."
Officials say large numbers of ground troops have been ordered to the border with Gaza.
An Israeli artillery unit also set up along Gaza's northern border.
On Saturday morning, the Israeli army said one strike had targeted a field used by Palestinian militants to fire rockets at Israel.
Earlier, during the dawn helicopter raids, the Israeli military said it had fired one missile at a Hamas weapons warehouse in the Jabaliya refugee camp.
Two more missiles were fired at targets in Gaza City.
The missiles appeared to have caused little damage but Palestinians said at least one person was injured.
The casualties in Sderot were caused by shrapnel from the Qassam rockets, one of which landed near a sports hall in the town centre.
Sderot is located near the border to the north-east of the Gaza Strip.
Islamic Jihad claimed responsibility for firing 10 home-made rockets into Israel on Friday, following the killing of three of its leaders by Israeli troops in Tulkarm.
Israel said the militants were killed after opening fire on troops who were trying to arrest them.
Israel's withdrawal from the Gaza Strip, completed on 12 September, ended 38 years of military occupation of the territory.