In its latest barrage, Israeli missiles struck a car before dawn. Three suspected Hamas fighters were killed as the vehicle burst into flames.
Israeli missles also hit several suspected arms factories, including several in the central town of Nusseirat.
The overnight offensive followed air raids during Saturday, in which a Palestinian boy was killed.
The 15-year-old boy was killed when an Israeli missile struck the Jabalya refugee camp in the northern Gaza Strip.
Ehud Olmert, the Israeli prime minister, on Sunday threatened stronger Israeli military steps in the Gaza Strip if Hamas fails to cease rocket attacks on southern Israel.
"If the measured steps we are taking, in the political and military sphere, do not bring about the desired calm, we will be forced to intensify our response," Olmert told his cabinet.
His comments came as Palestinian fighters fired five more rockets into Israel.
Also on Saturday, three men were killed when they were hit by a missile aimed at fighters launching rockets at Israel. Local residents said they were shepherds, but Israel said they were fighters.
The strikes came on a day when more than a dozen rockets were fired into Israel from the Palestinian territories. Nobody was hurt in Israel by the missiles, although they caused some damage in towns bordering the Gaza Strip.
Gaza residents said that three bystanders were also wounded in another missile strike in Gaza City when a missile struck a house.
Under attack from Israel, both Hamas and Fatah have ceased fighting each other.
Gunmen armed with rifles, grenades and explosives climbed down from rooftop positions on Saturday, and dozens of hostages kidnapped in a week of fighting between the the two rivals were released early on Sunday.
The respite allowed battle-weary residents to venture forth from their homes for the first time in days to buy groceries, or to return to homes abandoned during the clashes.
Truce enforcers from various Palestinian factions went from rooftop to rooftop in Gaza City, the centre of the fighting, urging gunmen to leave.
At one building that had been the site of fierce fighting, Hamas fighters climbed down carrying a cache of rocket-propelled grenades, bags of explosives and AK-47 rifles.
Mervat, a resident who would only give her first name for fear of reprisal, said the fighting terrorised her 5-year old daughter who thought the conflict was with Israelis. The two never left home throughout the fighting.
The hostage handover - a major element of the ceasefire deal - was delayed for hours while kidnapped men were located. Shortly after midnight on Saturday, two buses carrying kidnapped men from both sides pulled up to the Egyptian representative office in Gaza City, where the ceasefire was negotiated.
Some were released immediately, and others were to be freed later on Sunday. In all, 48 hostages were to be swapped, said Colonel Burhan Hamad, head of an Egyptian security team that helped to mediate the ceasefire.
Source: Al Jazeera and agencies