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Rishi Sunak has met the Palestinian Authority president in Egypt, as he continues his tour of the Middle East.
Mr Sunak and Mahmoud Abbas jointly condemned Hamas's attacks on Israel and the PM "expressed his deep condolences" for civilian deaths in Gaza.
He also met Egyptian President Abdul Fattah al-Sisi, agreeing the need to avoid a "contagion of conflict".
The PM welcomed efforts to reopen the Egypt-Gaza border, where some 20 aid trucks are poised to enter.
In a summary of the conversation between Mr Sunak and Mr Abbas, Downing Street said they "condemned Hamas's terrorism and stressed that Hamas do not represent the Palestinian people".
"The prime minister underscored his commitment to opening up humanitarian access to Gaza to alleviate the suffering of thousands of people who desperately need food, water and medicine," the statement added.
Mr Abbas is head of the Palestinian Authority, which has control over areas of the occupied West Bank, but not the Hamas-run Gaza Strip.
In his earlier meeting with President El-Sisi, Downing Street said Mr Sunak "praised Egypt's efforts in attempting to secure the delivery of aid" through the Rafah border crossing with Gaza.
The statement also noted the pair agreed "global leaders should do everything possible to avoid a contagion of conflict in the region" as well as make "every effort" to stop terrorism and protect civilians.
Before travelling to Egypt on Friday, Mr Sunak thanked the emir of Qatar for his efforts to help secure the release of hostages taken by Hamas.
Meeting in Saudi Arabia's capital Riyadh, Mr Sunak and Qatar's leader Sheikh Tamim bin Hamad Al Thani agreed to do "everything possible" to avoid an escalation of violence across the region, Downing Street said.
The United Nations says the first aid delivery into Gaza via the Rafah border crossing in Egypt is expected to take place "in the next day or so".
The territory has been under a "complete siege" since last Monday, with Israel blocking cross-border supplies of water, electricity and fuel.
Israeli warplanes and artillery have been bombarding the territory after more than 1,400 people were killed in Hamas's attack on Israel on 7 October. Palestinian officials say 3,700 people have since been killed in the Gaza Strip.
Dozens of trucks are backed up at the crossing on the Egyptian border, carrying food, water, and medicine but no fuel. It is believed only 20 will initially be allowed to cross.
More on Israel-Gaza war
Mr Sunak began his Middle East tour on Thursday, starting in Israel, where Mr Sunak said he was proud to support the country in its "long war" against Hamas.
On Thursday, Mr Sunak urged Saudi Crown Prince Mohammed bin Salman to support stability in the region.
Downing Street said the pair agreed the "loss of innocent lives in Israel and Gaza over the last two weeks has been horrific" and "underscored the need to avoid any further escalation in the region".
It came after a short visit to Tel Aviv, where he met with Prime Minister Benjamin Netanyahu and said he was "proud" to stand with Israel in its "darkest hour" - declaring the UK's backing for its fight against Hamas.
On Saturday, Egypt will host a summit on the future of the Palestinian issue, with Arab and UN leaders attending.