"The soldiers killed terrorists and directed air forces to real-time strikes on targets and terror infrastructure," the army said in a statement.
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 organisation," the statement said.
The fighting came after Netanyahu on Monday evening slapped aside a call from 120 countries for a sustained humanitarian truce.
"This will not happen," the premier told foreign media, vowing Israel would "fight until this battle is won."
"Calls for a cease-fire are calls for Israel to surrender to Hamas," he said.
Israel launched the war on October 7 in retribution for Hamas-led raids on Israeli homes, farms and villages that killed an estimated 1,400 people, according to Israeli officials.
More than three weeks of massive and sustained Israeli aerial bombardments have been followed by a large-scale ground offensive inside Gaza.
On Monday witnesses saw "dozens" of Israeli tanks operating on the southern outskirts of Gaza City.
Israel's military also released images of mechanized units grinding through coastal sands in northern Gaza.
They claimed an early victory: the rescue of one missing woman soldier from Hamas captivity.
The release of Private Ori Megidish was "secured during a ground operation" inside Gaza the army said, adding she was now in Israel, reunited with family and was "doing well."
"She has provided intelligence that we'll be able to use for future operations" said army spokesman Jonathan Conricus.
"We are committed and determined to get all of the 238 hostages that are still inside Gaza" he added.
'I found them all'
But the toll of Israel's war in Gaza has sparked a global backlash.
According to Gaza's Hamas-run health ministry, Israel's bombing campaign has killed more than 8,000 people, many of them children.
Thousands of buildings have been destroyed and the territory's 2.4 million residents have little access to water, food, fuel and other essentials.
Some 120 governments voted in favour of a non-binding U.N. resolution calling for a sustained truce.
On Monday, the U.N. agency for Palestinian refugees UNRWA said the limited number of aid trucks entering Gaza was insufficient to meet the "unprecedented humanitarian needs."
"Nearly 70% of those reported killed are children and women," said Philippe Lazzarini, who heads UNRWA. "This cannot be 'collateral damage."
Rizk Abu Rok, a 24-year-old paramedic with the Palestinian Red Crescent, told AFP that transporting those killed and wounded had become a daily routine.
But a recent strike on the Rio Cafe in Khan Yunis added his father and several other relatives to the growing toll.
"I found them all, one after the other," he said.
Israel has accused Hamas of using hospitals as military headquarters and civilians as "human shields," charges dismissed by the militants as "baseless" propaganda.
Even Israel's staunchest allies have voiced concern about the dire humanitarian situation inside the territory.
In Washington, the White House rejected a permanent cease-fire — warning it would only give Hamas time to restock and regroup.
But National Security Council spokesman John Kirby said "pauses" to allow aid into Gaza should be considered.
The United States has called for much more aid to enter Gaza from Egypt.
Israel said it is inspecting cargo to make sure weapons are not being smuggled in, and is monitoring to guarantee supplies are not seized by Hamas.
'Unfathomable horrors'
In Israel, citizens are still trying to comprehend the events of October 7.
Very little is known about the fate of the more than 230 hostages — aged between a few months and over 80 years old — who are believed to be held in a network of Hamas tunnels under Gaza.
Hamas on Monday released a video of what it claimed were three women hostages, seated against a tile wall.
One of the women called for Israel to agree to Hamas's demand to exchange the hostages for Palestinian prisoners held by Israel.
The time and place of the recording could not be verified.
Netanyahu decried the clip as "cruel psychological propaganda."
And even as Israel continues to be struck by daily rocket attacks from Gaza and Lebanon, Israelis have yet to account for all their missing and dead.
On Monday, authorities said the remains had been found of 23-year-old German-Israeli who was abducted from a music festival in the Israeli desert.
She had been "tortured and paraded around Gaza by Hamas terrorists" and "experienced unfathomable horrors," according to Israel's foreign ministry.
In the aftermath, images circulated of a young woman lying face down and nearly naked in the back of a pick-up truck filled with armed men.
Louk's family said they recognised Shani because of her dreadlocks and distinctive tattoos, but had held out hope she had survived despite her injuries.
Louk's sister Adi spoke of her "great sorrow" as she shared the news of Shani's death on social media.
'Axis of terror'
While Netanyahu has claimed Israel is "fighting Hamas" and an "Iranian axis of terror" that includes armed groups in Lebanon, Syria, Iraq and Yemen, Washington has expressed fears of a regional war.
The White House has warned Israel's enemies — in particular Iran-allied groups — not to become more involved.
Lebanese caretaker prime minister Najib Mikati told AFP it was his "duty to prevent Lebanon from entering the war."
All the while, Israel's military has struck targets in Syria and traded cross-border fire with Hezbollah in Lebanon, insisting Israel has a duty to defend civilians.
In the Israeli-occupied West Bank, health officials say about 120 Palestinians have been killed by Israeli fire and in settler attacks since the Gaza war started.
Amid the violence, anti-Israel anger has flared across the region and beyond.
In Russia's Muslim-majority Dagestan, police said they had arrested 60 people after a crowd stormed an airport on Sunday to attack passengers arriving from Tel Aviv.
Forum