Israel pounded Hamas rocket launchers, uncovered more than a dozen cross-border tunnels and engaged in gun battles with Palestinian militants Saturday on the second day of its open-ended ground operation in Gaza, as the Palestinian death toll there topped 300.

The Israeli military said that during its first 24 hours on the ground troops were mostly staying close to the border area and had discovered 13 tunnels into Israel - some as deep as 30 meters (yards) - that could be used to carry out attacks.

The military also said that in 12 days of fighting it has hit 2,350 targets in Gaza, including 1,100 rocket launchers, and severely diminished the arsenal of Hamas, the Islamic militant group that controls the coastal territory.

Militants have meanwhile fired more than 1,600 rockets since the latest round of fighting began on July 8. Rocket fire continued overnight, including one that landed in a residential neighborhood in the southern Israeli city of Ashdod, causing no injuries.

"We have struck hard on the two main strategic assets of Hamas: the rockets and these tunnels," said Israeli military spokesman Lt. Col. Peter Lerner.

Gaza Health Ministry spokesman Ashraf al-Kidra said overnight airstrikes raised the death toll from the 12-day offensive to more than 310 Palestinians, many of them civilians and about a fifth of them children. An Israeli soldier was killed after the start of the ground operation, likely from friendly fire, and an Israeli civilian was killed earlier this week.

Protest held in Temple Terrace

In Temple Terrace Friday night, Palestinian supporters waved flags, carried signs and chanted in solidarity.

"People like to call it a cycle of violence, but the real cause of the problem is the occupation," Palestinian supporter Ahmad Saadaldin said. "It's the arresting of innocent civilians, political prisoners, child prisoners. It's when American citizens are beaten or jailed. It's the occupation, the killing of innocent civilians that causes all the violence. 

"Once the occupation stops, you might see peace in the Middle East."

But some Israeli supporters say the attacks are just retaliation.

"Imagine if you were having missles thrown at your children, at your neighborhood and at your country. What would you expect your government to do?" Rabbi Laser Rifkin asked. "They need to stop attacking civilians with their missiles, which they started. Now, Israel is defending itself, which is the proper thing to do."

1 in 5 Gaza dead are children

Sobbing and shaking, Ismail Abu Musallam leaned against the wall of a hospital Friday, waiting for three of his children to be prepared for burial. They were killed as they slept when an Israeli tank shell hit their home, burying 11-year-old Ahmed, 14-year-old Walaa and 16-year-old Mohammed under debris in their beds.

His personal tragedy is not unique: the U.N. says minors make up one-fifth of the 299 Palestinians killed in 11 days of intense Israeli bombardment of the densely populated Gaza Strip, where half the 1.7 million people are under age 18.

The Israeli military says it's doing its utmost to spare civilians by urging residents to leave areas that are about to be shelled or bombed as Hamas targets. It accuses the Islamic militants of using civilians as human shields by firing rockets from civilian areas.

But even if urged to evacuate, most Gazans have no safe place to go, rights activists say.

"If you are going to attack civilian structures in densely populated areas, of course you are going to see children killed," said Bill Van Esveld, a researcher for New York-based Human Rights Watch.

Seventy-one of those killed since fighting began on July 8 were under 18, according to an Associated Press count based on information provided by Palestinian health official Ashraf al-Kidra. Forty-eight of the victims were under the age of 13.

Many of the children were killed in their own homes.

Early Friday, a 5-month-old baby boy was hit by shrapnel from a missile strike near his family compound in the southern town of Rafah. A day earlier, two brothers and a cousin were killed by shrapnel while feeding pigeons on the roof of their home.

One deadly incident drew particular outrage. Four cousins, aged 9 to 11, had been playing on the beach near Gaza City's harbor on Wednesday when a missile fired from an Israeli gunboat hit a nearby shack. The boys fled, but were killed in a second missile strike.

Information from the Associated Press was included in this report.