An Israeli rocket is fired into the northern Gaza Strip July 17, 2014 REUTERS/Amir Cohen

Israeli air strikes killed 11 people early on Saturday as the Jewish state's ground offensive to maim the "terror infrastructure" of Hamas entered the third day.

According to an emergency services spokesman, seven people died in a dawn attack near a mosque in the southern city of Khan Yunis.

Four more were killed in air strikes that followed, pushing the death toll in Gaza beyond 300 over 12 days of intense Israeli bombardment.

On Friday, Israeli Prime Minister Benjamin Netanyahu said he had asked the troops to prepare for a "considerable expansion of the ground operation".

"We chose to embark on this operation after exhausting the other options and with the understanding that without the operation, we could pay a much higher price," Netanyahu said.

Tel Aviv decided to back up its air offensive with a ground invasion in order to stamp out the threat of a network of tunnels that Hamas has built.

Israel believes the tunnels, which connect various supply sources and work as channels for smuggling in weapons, pose a long-term threat.

"There appears to be some misunderstanding of how severe the tunnel threat really is ... A successful attack through such a tunnel ... can turn everything around," Ma. Gen Gadi Shamni, a former commander of the Israel Defense Forces' Gaza Division, said, according to the Los Angeles Times.

Since the launch of the ground operation, Israel has uncovered 10 tunnels with 22 exit points across the Gaza Strip.

Meanwhile, the United Nations said Secretary General Ban Ki-moon will travel to the region seeking means to end the conflict, the worst in several years.

Ban will work with regional and international leaders and help Israelis and Palestinians in ending the violence, the UN said.