Witnesses reported deadly strikes overnight in Khan Yunis, the largest city in southern Gaza, and fierce fighting between Israeli soldiers and Hamas militants.
Netanyahu has vowed "complete victory" over Hamas after attacks by the Islamist movement's fighters on October 7 that resulted in the deaths of about 1,140 people, mostly civilians, according to an AFP tally based on official Israeli figures.
Hamas militants also seized about 250 hostages and Israel says around 132 remain in besieged Gaza.
The war has spurred fears of a wider escalation, and sirens were heard again overnight in northern Israel near the border with Lebanon, according to the Israeli military.
There have been almost daily exchanges of fire between Israeli forces and the Iran-backed Hezbollah movement in Lebanon, and several areas of southern Lebanon were hit overnight.
One such Israeli strike killed a Lebanese Hezbollah fighter, according to a source in the Hamas-aligned group.
Violence has also surged in the Israeli-occupied West Bank.
Huthi rebels in Yemen have also attacked what they deem to be Israeli-linked shipping in the vital Red Sea shipping lanes, prompting retaliatory US and UK strikes, while attacks in Syria and Iraq have mostly been claimed by Iran-linked militants opposing US support for Israel.
'Necessary step'
Hamas said in its first public report on the events that triggered the war there had been "some faults" on its part but also called for an end to "Israeli aggression" in Gaza.
The October 7 attacks were a "necessary step" against Israeli occupation of Palestinian territories and a way to secure the release of Palestinian prisoners, it said in its 16-page report.
Israel vowed to "annihilate" Hamas after the attacks and launched a relentless offensive that has killed at least 25,105 people in Gaza, mostly women and children, according to the Hamas-run health ministry in Gaza.
The Israeli campaign has killed "around 20 percent to 30 percent" of Hamas fighters and is still far from its goal of destroying the Islamist movement, according to estimates by US intelligence agencies, the Wall Street Journal reported on Sunday.
It said the United States, Qatar and Egypt, the countries that mediated a truce in November, were trying to convince Israel and Hamas to approve a plan that would free all the hostages in exchange for an Israeli withdrawal from Gaza.
Netanyahu has maintained that Israel must retain security control after the war and has rejected the possibility of "Palestinian sovereignty".
Major ally the United States and others have recommended that a so-called two-state solution was the only way to guarantee Israel's long-term security.
'Bring hostages back'
Netanyahu is also under intense pressure to secure the return of the hostages and account for security failings surrounding the October 7 attacks.
Relatives and supporters of the hostages again rallied near Netanyahu's Jerusalem residence in Jerusalem on Sunday night for their return.
"We are asking our government to listen, to sit down at the negotiating table and decide whether to accept this agreement or any other that would suit Israel," said Gilad Korenbloom, whose son is a hostage in Gaza.
John Polin, also the father of a hostage, said Israelis serve their country and in return "we expect the government to ensure our safety".
"We are asking the government to play its part, to propose an agreement, to bring it to a successful conclusion and to bring the remaining hostages back alive," Polin said.
Netanyahu said in a video statement released after the Hamas report that, in exchange for the release of Israeli hostages, Hamas was demanding an end to the war, the withdrawal of Israeli troops from Gaza, the release of Palestinian prisoners and guarantees that Hamas would stay in power.
"If we accept this, our soldiers have fallen in vain," and security would not be guaranteed, he said.
French Defence Minister Sebastien Lecornu was to meet families of Hamas hostages on Monday, before holding talks with Netanyahu and his Israeli counterpart Yoav Gallant.
Humanitarian crisis
UN agencies have warned of famine and disease as Gazans, 1.7 million of whom are displaced, struggle with shortages of water, medical care and other essentials during daily bombardment.
On Sunday, 260 humanitarian aid trucks were transferred to Gaza, according to COGAT, the Israeli defence ministry body responsible for Palestinian civilian affairs, well below pre-war levels.
Hamas's Qatar-based chief Ismail Haniyeh had met Turkey's foreign minister to discuss the conflict and humanitarian aid, diplomatic sources said on Sunday.
Abdelrahmane Iyad, wounded in Gaza and now being treated aboard the French helicopter carrier Dixmude, docked in Egypt, said he did not have time to leave his house before it was hit.
"When they bombed the house, I was thrown into the air and hit the wall of our neighbours' house. My leg was trapped under the broken ceiling, and a stone hit the front and back of my head. I lost consciousness," he said.
"I was with my parents, my brother, my sister, my second sister and her husband and their daughter. They all died. I'm the only survivor."
