Israel uncovered more than a dozen cross-border tunnels and engaged in gun battles with Hamas militants today 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 98ft (30m) – which could be used to carry out attacks.

WATCH: Video produced by the Israeli military purporting to show strikes on militants' tunnels:

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 which controls the coastal territory.

The militants, meanwhile, have 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 area in the southern Israeli city of Ashdod. No injuries were reported.

“We have struck hard on the two main strategic assets of Hamas: the rockets and these tunnels,” said Israeli military spokesman Lieutenant Colonel Peter Lerner.

Gaza Health Ministry spokesman Ashraf al-Kidra said overnight air strikes 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, probably by friendly fire, and an Israeli civilian was killed earlier this week.

Israel says it has encountered little resistance on the ground so far, and has killed about 20 militants in sporadic gun battles. Three soldiers were wounded in overnight fighting, one seriously, the military said.

In one case, it said troops encountered a man who appealed for medical assistance before pulling out grenades and trying to hurl them at soldiers. He was shot dead. Troops also encountered a donkey with explosives strapped to it.

Casualties could mount quickly if and when the military moves into urban areas.

Israel launched the ground operation late on Thursday after hundreds of air strikes on the Hamas-ruled territory failed to halt unrelenting rocket fire that has increasingly targeted major Israeli cities.

An Egyptian truce proposal was rejected by Hamas, which has ruled Gaza since 2007 and has demanded the lifting of an Israeli and Egyptian blockade as part of any ceasefire agreement.

In a fresh effort to broker a truce, UN chief Ban Ki-moon was due to travel to the Middle East today to help mediate the Gaza conflict.

A ceasefire is “indispensable” for urgently needed humanitarian efforts to succeed, under-secretary-general for political affairs Jeffrey Feltman told an emergency meeting of the Security Council yesterday.

Israeli officials have said the offensive could last up to two weeks. The military reported making steady progress but said dozens of tunnels remain and would not give a timeframe for its operation.

Israel’s military chief, Lieutenant General Benny Gantz, visited troops on the Gaza border early today and said “a strategic national patience is necessary” to complete the mission.

The sound of tank fire and heavy machine guns mixed with the mosques’ morning call to prayer along the Gaza-Israel border today.

Hamas said it has fired anti-tank missiles at Israeli troops. Gaza militants have remained defiant despite the rising death toll.

“The Palestinian people in the Gaza Strip will not surrender to the enemy and will not raise the white flag,” Ziad Nakhala, a leader in the Islamic Jihad militant group, told a Palestinian radio station.

“We are open to all possibilities as long as the enemy does not respond to the demands of the resistance.”

Hamas has survived Israeli offensives in the past, including a major three-week ground operation in January 2009 and another week-long air offensive in 2012, but in each case the militant group recovered. It now controls an arsenal of thousands of rockets, some long range and powerful, and it has built a system of underground bunkers.

But Hamas is weaker than it was during the previous two offensives, with little international or even regional support from its main allies, Turkey and Qatar.

Protests against the offensive took place in Turkey, Jordan and the West Bank yesterday.

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