Israeli forces killed at least 10 Palestinian militants on Monday after they crossed the border from Gaza through two tunnels, the military said, as the death toll from the two-week conflict passed 500.
With the U.N. Security Council calling for an immediate ceasefire, Israeli jets and tanks continued to pound the Gaza Strip through the night.
The Israeli barrage killed 25 people from one family near Gaza's southern border with Egypt, while 10 from another died in the nearby Khan Younis after shells hit their home and struck again as they tried to flee, hospital officials said.
The overnight raids lifted the Palestinian death toll to 484, mostly civilians, since fighting started on July 8. Israel says 18 of its soldiers have also died along with two civilians.
In New York, the Security Council called for a truce after an emergency meeting on Sunday. The 15-member Council "expressed serious concern about the growing number of casualties (and)... called for an immediate cessation of hostilities," Rwanda's U.N. Ambassador Eugene Gasana told reporters.
Two groups of Palestinian fighters slipped into southern Israel in the early morning, with the Israeli army ordering a lockdown in local communities as they tracked them down.
Aircraft targeted one of the squads and soldiers opened fire on the other, killing at least 10 militants, a military spokeswoman said. The military had no immediate comment on media reports of casualties amongst Israeli forces.
Fighters from the Hamas Islamist group, which runs Gaza, and its allies, have repeatedly tried to enter Israel over the past week through a vast network of hidden tunnels, looking to attack villages and army encampments that dot the border area.
Israeli Prime Minister Benjamin Netanyahu order his ground forces into Gaza on Thursday, promising to destroy the tunnels and put an end to incessant missile fire out of the populous Mediterranean enclave.
Setting off celebrations around Gaza, Hamas's military wing announced on Sunday that it had captured an Israeli soldier during fighting. It named the man as Shaul Aron and showed his ID papers, but showed no picture of him in their hands.
Although Israel's ambassador to the United Nations denied the claim, Israel's military said it was still investigating.