Israel has widened its range of Gaza bombing targets to civilian institutions with suspected Hamas ties and announced it would hit northern Gaza "with great force" to prevent rocket attacks from there on Israel.
More than 150 Palestinians have been killed so far in five days of bombardment.
One of the Israeli strikes hit a centre for the disabled where Palestinians said two patients were killed and four people seriously hurt.
In a second attack, an Israeli plane flattened the home of Gaza's police chief and damaged a nearby mosque as evening prayers ended, killing at least 18 people, officials said.
Israel has carried out more than 1,200 air strikes this week, and a military spokesman said there would be more strikes, especially in northern Gaza near the Israeli border.
"We are going to attack there with great force in the next 24 hours due to a very large concentration of Hamas efforts in that area," the spokesman said.
The military said it was ordering Palestinians in northern Gaza to evacuate "for their own safety".
Gaza's Interior Ministry urged residents in the area to ignore Israel's warnings and stay in their homes, saying the announcement was Israeli "psychological warfare" and an attempt to create confusion.
Shortly after the Israeli announcement, an Israeli plane struck the home of the Gaza police chief, Taysir al-Batsh, killing at least 18 people and wounding 50, said Health Ministry official Ashraf al-Kidra.
He said worshippers were leaving the mosque after evening prayers at the time of the strike and that some people are believed to be trapped under the rubble.
Hamas, the Islamic militant group that controls Gaza, has fired nearly 700 rockets and mortars at Israel this week and said it would not be the first to cease fire.
In a sign that the conflict might widen, Israel fired into Lebanon this evening in response to two rockets fired from there at northern Israel. There were no injuries or damage, but Israel fears militant groups in Lebanon could try to open a second front.
Israel has said it is acting in self-defence against rockets that have disrupted life across much of the country. It also accuses Hamas of using Gaza's civilians as human shields by firing rockets from there.
Critics said Israel's heavy bombardment of one of the most densely populated territories in the world is the main factor putting civilians at risk.
Sarit Michaeli of the Israeli human rights group B'Tselem said that while using human shields violates international humanitarian law, "this does not give Israel the excuse to violate international humanitarian law as well".
The Israeli military said it has targeted sites with links to Hamas, including command centres, and that it issues early warnings before attacking.
But Ms Michaeli said civilians have been killed when Israel bombed family homes of Hamas militants or when residents were unable to leave their homes quickly enough following the Israeli warnings.
Before dawn today, an Israeli missile hit the Palestine Charity, a centre for the physically and mentally disabled in the northern Gaza town of Beit Lahiya, said its director, Jamila Alaiweh.
The centre was home to nine patients, including four who were spending the weekend with their families away from the centre, said Ms Alaiweh.
Of the remaining five, two were killed in the strike and three suffered serious burns and other injuries, the director said. A caregiver was also injured, she added.
The director said one of the women killed had cerebral palsy and the other was severely mentally disabled. Among the three wounded patients were a quadriplegic, one with cerebral palsy and one with mental disabilities, she said.
An army statement said that from Friday morning to Saturday morning, Israel targeted 158 targets "affiliated with Hamas terrorism" in Gaza, including dozens of rocket launchers and a mosque where Hamas stored rockets and weapons.
Israel also targeted several civilian institutions with presumed ties to Hamas, widening its range of targets.
Palestinian officials said this included a technical college, a media office, a small Kuwait-funded charity and a branch of an Islamic bank.
Mr al-Kidra said Israeli strikes raised the death toll there to more than 150, with over 920 wounded.
Among the dead was a nephew of Ismail Haniyeh, a senior Hamas leader, who was killed in an air strike near his home, Hamas officials said.
Though the exact breakdown of casualties remains unclear, dozens of the dead have been civilians. Israel has also demolished dozens of homes it says are used by Hamas for military purposes.