It came after thousands of Palestinians fled their homes in the northern part of the territory following warnings of attacks on rocket-launching sites.
The move occurred on the sixth day of an offensive that Palestinian officials said has killed at least 160 people.
Militants in the Hamas-ruled strip continued to discharge rockets deep into the Jewish state and the worst bout of Israel-Palestinian bloodshed in two years showed no signs of abating.
Israeli prime minister Benjamin Netanyahu said he would be “restoring calm for a long period by dealing a significant blow to Hamas and other terrorist groups in the Gaza Strip”.
Western leaders, including foreign minister William Hague, called for a ceasefire.
Mr Hague has warned of the “urgent need” to end the fighting as Israel used ground forces for the first time in the current offensive. Israeli troops were deployed on a brief raid into northern Gaza and airstrikes were targeted at security headquarters as the response to waves of rocket strikes launched by Hamas was ramped up.
Earlier in the day, Israeli forces dropped leaflets into the town of Beit Lahiya near Gaza’s northern border with Israel. They read: “Those who fail to comply with the instructions to leave immediately will endanger their lives and the lives of their families. Beware.”
The Israeli military told the residents of three of Beit Lahiya’s ten neighbourhoods to get out of the town of 70,000 by midday yesterday. United Nations officials said some 4,000 people had fled south to eight of its schools in Gaza City. A senior Israeli military officer said Israel would “strike with might” in the Beit Lahiya area from late evening yesterday.
He did not say if this would include the expansion of an air and naval offensive into a ground operation in the densely populated Mediterranean enclave. The officer added: “The enemy has built rocket infrastructure between the houses [in Beit Lahiya]. He wants to trap me into an attack and into hurting civilians.”
At schools run by the UN Relief and Works Agency in Gaza City, Beit Lahiya residents arrived in donkey carts filled with children, luggage and mattresses, while others came by car or taxi. Salem Abu Halima, 25, a father of two, said: “What could we do? We had to run in order to save the lives of our children.”
The Gaza interior ministry dismissed the Israeli warnings as “psychological warfare” and instructed those who left their homes to return and others to stay put.
The leaflets marked the first time Israel had warned Palestinians to vacate dwellings in such a wide area. Previous warnings, by telephone or so-called “knock-on-the-door” missiles without explosive warheads, had been directed at homes targeted for attack.
Early yesterday, a Palestinian woman and a three-year-old girl were killed in Israeli air strikes. Hours previously, 17 people were killed when the house of Gaza’s police chief was bombed.
The health ministry said at least 160 Palestinians, including 135 civilians – among them some 30 children – have been killed in six days of warfare and more than 1,000 have been wounded.
Hostilities along the Israel-Gaza frontier intensified last month after Israeli forces arrested hundreds of Hamas activists in the Israeli-occupied West Bank following the abduction there of three Jewish teenagers who were later found killed. A Palestinian youth was then killed in Jerusalem in a suspected revenge attack by Israelis.