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A representative of the organisation told the BBC that Hamas accepted the proposal in principle - but wished to make some changes on a number of key points. We ask the experts what this might mean for a peace deal in the Middle East.
Also in the programme: rap star Sean 'Diddy' Combs sentenced to 50 months on sex-related charges in a New York court; prominent French economist Gabriel Zucman explains his proposal for a wealth tax; and the first female archbishop of Canterbury.
(Photo: Israeli military operation in Gaza City, 3 October 2025; Credit: MOHAMMED SABER/EPA/Shutterstock)
Dame Sarah Mullally has been named as the new Archbishop of Canterbury designate - the first woman to be chosen to head the Church of England.
It is the first time in nearly 500 years of history that the Church has nominated a woman as its head. We'll ask who Sarah Mullally is - and whether she can restore trust and unity in her church.
Also in the programme: A senior member of the Jewish community in the UK says Thursday's deadly attack in Manchester was a shock but no surprise; we'll hear about tourism creaking in Cuba; and a ravenous baby planet has been making headlines.
The British Prime Minister Keir Starmer says Britain must defeat what he called the "rising hatred of Jewish people", after a deadly attack at a synagogue. Two Jewish people were killed and four others injured after a car was driven towards worshippers at the site in Manchester. Police declared it a terrorist incident. They shot the suspect dead.
Also in the programme: Venezuela's opposition leader tells us she welcomes America's attacks on alleged drug smugglers, saying they'll force the President out. We look at protests in Morocco; and is Formula One getting too hot for the safety of its drivers?
(Photo: A member of the Jewish community holds a Torah at a police cordon in Manchester, Britain, 2 October 2025. Credit: Photo by Adam Vaughan /EPA/ Shutterstock)
Two people have been killed by a car that drove into a crowd outside a British synagogue on the Jewish holy day of Yom Kippur. Another man was stabbed at the site. We hear the latest news on the incident.
Also in the programme: a wide-ranging interview with the leader of the Venezuelan opposition, Maria Corina Machado, who is in hiding after being barred from last year's election; and a BBC analysis of Ukrainian drone attacks against Russian oil refineries.
We also hear about a new exhibition in Cambridge that sheds light on craftspeople in ancient Egypt.
(Photo: People gather near the scene following an incident outside a synagogue in Manchester, Credit: REUTERS/Temilade Adelaja)
EU leaders are meeting in Copenhagen under pressure to boost European defence after a series of Russian incursions into EU airspace, and days after drones targeted Danish airports.
Also in the programme: The International Red Cross has been forced to cease operations in Gaza City because of the intensity of the Israeli offensive; Jane Goodall, famous for her ground-breaking studies of chimpanzees, has died at the age of 91; and as one Hollywood star, Julie Andrews, turns 90, we'll hear about a new young actor who'll never grow old.
(Photo: Denmark has reinforced security for the summit and allies have beefed up air defences. Credit: Reuters)
The International Red Cross has been forced to cease operations in Gaza City because of the intensity of the Israeli offensive. It’s continuing while Arab and Turkish mediators put pressure on Hamas to accept President Trump's peace plan.
Also on the programme: we'll hear from the city at the epicentre of the earthquake in the Philippines where there's only one hospital to deal with the casualties; and the AI-generated actress causing a stir in Hollywood.
(Photo: Displaced Palestinians fleeing northern Gaza due to an Israeli military operation, after Israeli forces ordered residents of Gaza City to evacuate to the south, 1 October, 2025. Credit: Reuters)
The United Nations has appealed to the Taliban to immediately restore telecommunications across Afghanistan. UN officials said the ban had far-reaching consequences, including on the banking and financial systems. Access to emergency services and medical care has also been hit. Mobile phone services are still not working and many flights have been cancelled. We'll hear from an Afghan activist about the impact this will have on daily life, and our chief International Correspondent Lyse Doucet.
Also in the programme: the US Defence Secretary Pete Hegseth declares a war on woke in the military; and scientists have made early stage human embryos from DNA taken from skin cells, raising the prospect of new fertility treatments.
(Picture: Telecom antennas stand on a mountain amid service shutdown across the country in Kabul, Afghanistan, September 30, 2025. Credit: Sayed Hassib/REUTERS)
Can Donald Trump's peace plan for Gaza work? The focus today is on Hamas' response. One Israeli lawmaker tells us he's sceptical. We also get reaction from Gaza City and analysis from the former State Department advisor and negotiator on the Middle East, Aaron David Miller.
Also in the programme: the Taliban turn off the internet in Afghanistan; and a new exhibition on the astonishing life of the artist and Second World War photographer Lee Miller.
(IMAGE: US President Trump and Israeli Prime Minister Netanyahu press conference at the White House, Washington, USA - 29 Sep 2025 / CREDIT: Jim Lo Scalzo/POOL/EPA/Shutterstock)
President Trump says the Israeli Prime Minister has agreed to his peace plan to end the war in Gaza. It's been drawn up following extensive talk with US allies in the Middle East, and provides for an end to the fighting once it's accepted by Israel and Hamas.
Also in the programme: we explores the hopes and obstacles of Moldova joining the European Union; and President Trump has threatened to impose one-hundred percent tariffs on movies made outside the United States.
(Picture: Israeli Prime Minister Benjamin Netanyahu and US President Donald Trump participate in a joint press conference at the White House on 29 September, 2025. Credit: WILL OLIVER/POOL/EPA/Shutterstock)
President Trump has expressed renewed optimism about reaching a deal to end the war in Gaza, ahead of talks on Monday with the Israeli Prime minister Benjamin Netanyahu. In a social media post, Mr Trump said there was a 'real chance for greatness in the Middle East'. He's subsequently said that he's received what he called a 'very good response' from Israel and Arab leaders to a new US proposal that he says is aimed not just at Gaza but at reaching a broader peace in the region.
Also in the programme: Misinformation has disrupted a vaccination programme in Pakistan against cervical cancer; we take a look at today's elections in Moldova; and we hear from a very bad tempered Ryder Cup!
(Photo: Residents of Gaza City are still evacuating as the fighting intensifies. Credit: Ali Jadallah/Anadolu via Getty Images)
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