It was the first major Israeli ground offensive in Gaza in just over five years and came after Egyptian-led efforts to broker a cease-fire failed. Earlier Thursday, 13 Hamas militants tried to infiltrate Israel through a tunnel under the Gaza-Israel border, but were stopped by an Israeli strike at the mouth of the tunnel.
The military said the operation was open-ended and would be carried out on several fronts in the coastal strip.
"Our forces, large ground forces accompanied by massive air force support, naval forces and intelligence, are taking over targets in Gaza, operating against tunnels and terror activists and infrastructure," Israel's chief military spokesman Brig. Gen. Motti Almoz said.
He called on Gaza residents to evacuate areas where the military is operating, warning the "military is operating there with very great force."
Thousands of soldiers backed by tanks and huge DC9 bulldozers entered the Hamas-ruled territory after 10 p.m. Thursday, security officials and Israeli media said.
Hamas spokesman Fawzi Barhoum said Israel "will pay dearly" for the assault. "Hamas is ready for a confrontation," he said.
An official in the Gaza security operations room reported heavy Israeli tank shelling along Gaza's border areas with Israel since 8 p.m. Thursday.
"All border areas are under fire. There is a tank shell every minute," said the official, speaking on condition of anonymity in line with briefing regulations. "There is also fire from the sea toward police checkpoints."
Thousands of Israeli soldiers had massed on the border with Gaza in recent days, waiting for the order to go in. Israel had called up 48,000 reserve soldiers and Lt. Col. Peter Lerner, another Israeli military spokesman, said more could be called up.
The ground operation followed a brief truce earlier Thursday in which Israel held fire to allow Gazans to stock up on food and other necessities after being largely holed up at home since the conflict began last month.
Since July 8, Israeli strikes have hit more than 2,000 targets in Gaza and Hamas launched nearly 1,500 rockets at Israel, the Israeli military has said.
Israeli Prime Minister Benjamin Netanyahu's office said he instructed the army to go ahead after Hamas rejected an Egyptian cease-fire plan earlier in the week and after Hamas militants tried to infiltrate into Israel through a tunnel from Gaza.
"In light of the despicable and relentless aggression by Hamas and the dangerous infiltration into Israel, Israel is obliged to protect its citizens," the statement said.
Israel last carried out a major ground offensive in Gaza in January 2009. The ground operation came toward the end of a three-week military campaign.