Israeli strikes killed at least 21 people in Gaza on Sunday, including six children, Palestinian health authorities said, ahead of a visit to the region by U.S. Secretary of State Antony Blinken to try to push forward ceasefire talks.

The children and their mother were killed in an Israeli airstrike on a house in the central town of Deir al-Balah, health officials said. There was no immediate comment from the Israeli military.

The Israeli military said it destroyed rocket launchers used to hit Israel from the southern city of Khan Younis, the scene of intense fighting in recent weeks, and killed 20 Palestinian fighters.

Diplomatic efforts to halt the Israel-Hamas conflict and secure a deal to return hostages held in Gaza have intensified in recent days. Talks mediated by the U.S., Egypt and Qatar are set to continue this week in Cairo, following a two-day meeting in Doha last week.

Making his 10th trip to the region since the war began, Blinken was due in Israel on Sunday, days after the United States put forward bridging proposals that the mediating countries believe would close gaps between the warring parties.

There has been increased urgency to reach a ceasefire deal amid fears of a regional escalation. Iran has threatened to retaliate against Israel after the assassination of Hamas leader Ismail Haniyeh in Tehran on July 31.

Israel is engaged in complex negotiations for the return of its hostages held in Gaza but also has principles to uphold that are vital for its security, Prime Minister Benjamin Netanyahu said at the start of a cabinet meeting on Sunday.

"There are things we can be flexible about, and there are things we cannot be flexible about, and we insist on them. We know very well how to differentiate between the two," he said.

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David Satterfield, former U.S special envoy for Middle East humanitarian issues, says current negotiations are more complicated than any conflict he's seen in his 45 years on the file.

At Al-Aqsa Hospital in Deir al-Balah, relatives gathered around the bodies of the mother and her six children, who were wrapped in white shrouds bearing their names. The youngest was aged 18 months, their grandfather Mohammed Khattab told Reuters at the funeral.

Israel has denied targeting civilians as it hunts down Hamas militants, accusing the group of operating from civilian facilities including schools and hospitals. Hamas denies this.

After 10 months of war, Palestinians in Gaza continue to feel pressure to find a safe place.

2 locations described as 'pressure cookers'

"We are tired of displacement. People are being pushed into narrow areas in Deir al-Balah and Al-Mawasi, which have become pressure cookers," Tamer Al-Burai, who lives in Deir al-Balah with several relatives, told Reuters via a chat app. Tanks were just 1.5 kilometres away, Burai added.

On Friday, the military ordered the evacuation of areas north of Khan Younis and east of Deir Al-Balah where hundreds of thousands of people displaced by the fighting had been sheltering in dire conditions.

The United Nations Office for the Coordination of Humanitarian Affairs said Friday's orders, which included other enclave areas outside the humanitarian zones, had reduced the size of the "humanitarian area" designated as safe by Israeli forces to about 11 per cent of the total area of the Gaza Strip.

WATCH | Palestinians leave Khan Younis after Israeli airstrikes:

Latest strikes in Gaza hit Hamad Towers in Khan Younis

Hundreds of displaced Palestinians streamed out of Khan Younis on Friday after several residential buildings were hit, which came after Israel Defence Forces dropped leaflets warning of a strike. Those who left described running amid heavy fire and said they had nowhere to go.

The Deir al-Balah municipality, estimating the current population in the city at one million, said the evacuation orders meant more people were crammed into a smaller space.

Additionally, water shortages loomed as several water wells and tankers that used to provide residents with 60 per cent of supplies were located in the areas under evacuation orders, the municipality said in a statement on Sunday.

'Cautious optimism' a deal can be reached

In Israel, Blinken is expected to meet with the Israeli prime minister and other senior officials.

Netanyahu's office said in a statement on Saturday there was "cautious optimism" a deal could be reached and U.S. officials have also been positive, while cautioning there was still work to be done.

However, Hamas said optimistic U.S. comments were "deceptive" and accused Netanyahu of making new conditions in an attempt to "blow up" the negotiation.

Hamas wants a ceasefire deal to end the war, while Israel wants a temporary pause.

The war erupted on Oct. 7 when Hamas-led fighters rampaged into Israel, killing around 1,200 people and seizing around 250 hostages, according to Israeli tallies.

Israel's subsequent military campaign has killed more than 40,000 Palestinians, mostly civilians, according to Palestinian health authorities, and reduced much of Gaza to rubble. Israel says it has killed 17,000 Hamas fighters.