Israel is prepared to "significantly widen" its ground offensive against militants in the Gaza Strip, Prime Minister Benjamin Netanyahu has said.
He said the military was targeting the Hamas tunnel network, which it could not do "only from the air".
Thousands of troops moved into parts of Gaza on Thursday night, backed by tanks and artillery fire.
Hamas, the Palestinian group that controls Gaza, has said Israel will "pay a high price" for the invasion.
The BBC's Yolande Knell in Gaza City says Israeli aircraft and artillery have intensified strikes in the north, east and south of Gaza.
Meanwhile, air raid sirens sounded in towns across southern Israel as rocket attacks from Gaza continued.
The UN said the number of people displaced by the conflict in Gaza had nearly doubled on Friday, from 22,000 to more than 40,000.
At least 24 Palestinians and one Israeli soldier have been killed since the ground offensive began on Thursday, Gaza's health ministry said.
"The ground invasion is a bad move because it is going to kill more innocent civilians and would do no good for Israelis." - Abdelraziq, business and management graduate, Gaza
"The ground invasion is a necessary evil. The last thing that Israel would like to do is to risk the lives of its own soldiers and the lives of innocent people, but we have to stop the firing of the rockets and destroy the tunnels." - Doron Youngerwood, marketing manager, Modiin, Israel
The dead included three Palestinian children killed by Israeli tank fire in the north of Gaza, medics added.
The Israel Defense Forces (IDF) say they struck more than 100 targets in Gaza overnight that included 20 missile launchers.
On Friday, the military announced it had arrested 13 militants and uncovered 10 tunnels since the start of the ground incursion.
The decision to send in troops came after 10 days of intensive rocket fire from militants in Gaza and air strikes by Israel.
"Last night our forces began a ground operation to hit the terror tunnels crossing from Gaza into Israel's territory," Mr Netanyahu told a special cabinet session broadcast live on television on Friday.
"It is not possible to deal with the tunnels only from the air."
He added: "My instructions... are to prepare for the possibility of significantly widening the ground operation, and the military is preparing accordingly."
Mr Netanyahu said the operation came after Israel had agreed to an Egyptian proposal for a ceasefire and to Thursday's five-hour UN humanitarian ceasefire.
"In both of these opportunities Hamas continued to fire," he said.
Palestinian militants have used tunnels to carry out attacks, some of which have been thwarted by the Israeli military.
On the morning of the ground offensive, the Israeli military intercepted 13 militants who had infiltrated Israel through a tunnel, and were believed to be planning to attack a nearby kibbutz.
Some 271 Palestinians - three-quarters of them civilians - have died since the start of the wider Israeli operation on 8 July, officials in Gaza say.
One Israeli civilian has been killed by mortar fire and several Israelis have been seriously injured, Israeli medics say.
Hamas spokesman Sami Abu Zuhri reacted defiantly to the Israeli offensive, declaring: "Netanyahu is killing our children and will pay the price. The ground invasion doesn't frighten us and the occupation army will sink in Gaza's mud."
Meanwhile, Palestinian Authority President Mahmoud Abbas, whose Fatah party recently agreed to a unity government with Hamas, has been holding talks in Cairo amid efforts to negotiate a truce.
On Friday he met leaders of Islamic Jihad, a smaller militant faction in Gaza, and said he found "a kind of acceptance" of the peace initiative.
Call for restraint
French Foreign Minister Laurent Fabius is travelling to Egypt, Jordan and Israel as part of a diplomatic push to stop the fighting.
On Thursday, Israel approved the drafting of 18,000 more reservists, bringing the number of extra troops called up since 8 July to 65,000.
Israel says it has carried out more than 1,960 attacks on Gaza since 8 July, while militants have fired some 1,380 rockets at Israel. It says more than 50 rockets have been fired at Israel since the ground operation began.
The UN says at least 1,370 homes have been destroyed in Gaza and more than 18,000 people displaced in recent hostilities.
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