Ignoring international appeals for a ceasefire, Israel also widened its range of Gaza bombing targets to civilian institutions with suspected Hamas ties.
More than 156 Palestinians have been killed in five days of bombardment.
Four Israeli soldiers were hurt in clashes during the brief incursion to destroy a rocket launching site in northern Gaza.
It was the first time Israeli ground troops are known to have entered Gaza in the current offensive. However, the operation was carried out by special forces and did not appear to be the beginning of a broad ground offensive.
One of the biggest Israeli strikes over the weekend hit a centre for disabled people, where Palestinians said two patients were killed and four people seriously hurt.
An Israeli warplane also flattened the home of Gaza's police chief and damaged a nearby mosque as evening prayers ended, killing at least 18 people.
The UN Security Council called unanimously for a ceasefire, and UK Foreign Secretary William Hague said he would today discuss ceasefire efforts with his American, French and German counterparts.
So far, rulers of neither Israel nor Hamas, the Islamic militant group that controls Gaza, have signalled a willingness to stop.
Israel has carried out more than 1,200 air strikes in the last week to try to diminish Hamas's ability to fire rockets at Israel.
The chief military spokesman, Brigadier General Motti Almoz, said there would be more strikes, especially in northern Gaza near the Israeli border.
He said: "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 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 to stay in their homes, saying the announcement was Israeli "psychological warfare" and an attempt to create confusion.
Shortly after the Israeli announcement, an Israeli warplane struck the home of Gaza police chief Taysir al Batsh, killing at least 18 people and wounding 50.
Health ministry official Ashraf al Kidra said worshippers were leaving a nearby mosque after evening prayers at the time of the strike and some people are believed to be trapped under the rubble.
Meanwhile, Hamas has fired nearly 700 rockets and mortars at Israel in the last few days and said it would not be the first to cease fire.
In a sign that the conflict might widen, Israel also fired into Lebanon in response to two rockets fired from there at northern Israel.
There were no injuries or damage, but Israel fears militant groups in Lebanon may try to open a second front.
Israel has said it is acting in self-defence against rocket attacks 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 itself the main factor putting civilians at risk.
Sarit Michaeli, of the Israeli human rights group B'Tselem, said that while using human shields violated international humanitarian law, "this does not give Israel the excuse to violate international humanitarian law as well".
The Iron Dome, a US-funded, Israel-developed rocket defence system, has intercepted more than 130 incoming rockets, preventing any Israeli fatalities so far. A handful of Israelis have been wounded by rockets that slipped through.
Air raid sirens have again been heard in Jerusalem and Tel Aviv, Israel's two largest cities, both located nearly 50 miles from Gaza.
Most of the rockets were intercepted or fell in open areas, though one landed near the Palestinian city of Hebron in the West Bank. A house was damaged but there were no injuries.
The frequent rocket fire has disrupted daily life in Israel, particularly in southern communities that have absorbed the brunt of it.
Frequent airstrikes have turned bustling Gaza City into a virtual ghost town during the normally festive month-long Ramadan holiday, emptying streets, closing shops and keeping hundreds of thousands of people close to home where they feel safest from the bombs.