Israel Prime Minister Benjamin Netanyahu has rejected international calls for a ceasefire in its war with Hamas terrorists hiding in Gaza Strip as the country's forces roll in the Palestinian territory and freed one hostage.

"Calls for a ceasefire are calls for Israel to surrender to Hamas, to surrender to terrorism," Netanyahu said, slapping aside demands from United Nations agencies and 120 countries for a truce.

"This will not happen," the premier told foreign media, vowing Israel would "fight until this battle is won."

Israel declared war on Palestinian militant group Hamas after it launched an unprecedented wave of attacks inside Israel on 7 October, killing more than 1,400 people, mostly civilians, and taking more than 230 people hostage.

Israel has since carried out a huge aerial bombing campaign against Hamas-ruled Gaza, while inside the territory, a long-expected ground war was underway.

The military has released images of Israeli mechanized infantry grinding through the coastal sands of northern Gaza, while witnesses on Monday reported tanks on the outskirts of Gaza City.

"The soldiers killed terrorists and directed air forces to real-time strikes on targets and terror infrastructure," Israel's army said in a statement issued Tuesday.

In the fourth night of major ground operations inside the north of the Palestinian territory, it reported "several engagements" in which its forces came under anti-tank missile and machine gun fire.

Air strikes hit about 300 targets including missile and rocket launch posts and "military compounds inside underground tunnels belonging to the Hamas terrorist organization," the statement said.

Israel also said a missing woman soldier was rescued from Hamas inside Gaza.

The release of Private Ori Megidish was "secured during a ground operation" inside Gaza the army said, adding she was in Israel, reunited with family and was "doing well."

Netanyahu has vowed the war will "eliminate" Hamas, ensuring no possible repeat of the group's attacks.

Israel has also promised to free the hostages taken by Hamas and other Palestinian militant groups.

Israel's campaign has flattened thousands of buildings and Gaza's 2.4 million residents are under near continuous bombardment, with little access to water, food, fuel and other essentials.

The UN has repeatedly called for a humanitarian truce in the violence, which the Hamas-run health ministry in Gaza claims has killed more than 8,000 people, many of them children.

On Monday, the UN agency for Palestinian refugees UNRWA said the limited number of aid trucks entering the besieged territory were insufficient to meet the "unprecedented humanitarian needs" there.