Israel at war: What happened on day 34?

Palestinian Islamic Jihad is willing to release two Israeli hostages they are holding, the terror group's spokesperson announced on Thursday, according to Israeli media reports. 

The spokesperson said that an elderly woman and a child could be released. They were later named as Hanna Katzir, 77, and Yagil Yaakov, 12, both of Kibbutz Nir Oz. Yaakov was kidnapped alongside his father, his father's partner, and his brother Or, 16.

Senior Hamas officials including political leader Ismail Haniyeh and its former chief Khaled Meshaal arrived in Cairo on Thursday, a statement by the Palestinian Islamist group that controls the Gaza Strip said.

The high-level Hamas delegation met with the head of Egypt's General Intelligence Service, Abbas Kamel, and discussed the situation in Gaza, the statement added.

Sirens sounded throughout northern Israel as several mortar shells were fired from Lebanon to Israel on Thursday evening.

IDF soldiers responded and struck the launcher from which the mortar shells were fired. 

Several anti-tank missiles were fired toward an IDF post in the area of Metula, next to the Lebanese border earlier on Thursday, to which the IDF also responded in kind. 

Israeli troops have cleared significant areas in the center of Gaza City that were the military headquarters of Hamas, the IDF announced on Thursday afternoon.

Soldiers from the Givati Brigade, along with the 162nd Armored Division and special forces, raided the military quarter which is situated near the Shifa Hospital and managed to kill 50 Hamas members during fierce combat. Israeli forces also secured and neutralized a wide underground network of tunnels.

The president of Cyprus outlined a proposal on Thursday to open a maritime corridor to help deliver more aid to Gaza, a plan which he said could be operational quickly but which diplomats said faced challenges.

Under the plan presented by President Nikos Christodoulides at a humanitarian conference in Paris, aid would be sent by sea to Gaza from the Mediterranean island of Cyprus, the closet European Union member state about 370 km (230 miles) away.

"We hope immediately to implement it," he said of the 25-page proposal.

Israel's public defense refuses to represent the October 7 terrorists who were captured and await trial, they announced on Thursday.

"Thus far, no lawyer from the public defense has been appointed to a single case of Hamas terrorists or any other terrorist-related to October 7," said the Public Defenders' Office. "In our opinion, the procedure against these terrorists is not suited to the judicial procedure available today to deal with terrorists and terrorism."

The office added that in the current situation, a solution was needed for a judicial system that suited the extreme circumstances.

The Hamas-run Gazan Health Ministry said Sunday that 10,812 Palestinians, among them 4,412 children, had been killed so far as a result of the war with Israel that began with Hamas's terrorist attack in Israel on October 7. 

On Sunday, the ministry reported 4,800 children killed, about 400 more than their current figure.

The IDF published a phone number alongside a Telegram channel for Gazan residents to report when Hamas terrorists are preventing them from fleeing southwards.

The phone number to contact is +972 50-341-0322 and the Telegram account is called: @gaza_saver.

The Committee on Foreign Affairs and Global Health on Capitol Hill, led by Congressman Chris Smith (R-NJ), took aim at the United Nations' long-standing bias against Israel on Wednesday. The focal point of this gathering was the United Nations Relief and Works Agency (UNRWA) and its troubling promotion of antisemitism among Palestinian youth.

Representative Smith delivered a powerful message, highlighting the urgency of addressing this issue. He emphasized the need for the United States and the international community to hold the UN accountable for its actions and to demand an end to these biased practices.

"Recent genocidal atrocities committed by Hamas, including acts of terrorism and indiscriminate missile attacks, are a direct outcome of the unbridled antisemitism fomented and enabled by the United Nations. Israel has an absolute right to defend itself against such cowardly invasions and massacres," Smith declared.

The head of the Mossad David Barnea, CIA chief William Burns and Qatari Prime Minister Mohammed Al Thani met in Doha on Thursday to discuss the situation surrounding the Israeli hostages held by Hamas, according to initial media reports.

The advantage of the trilateral meeting was to bring all three parties together at one table in real time to speed up the process, a source briefed on the meeting told Reuters.

The talks, according to the same source, also included a discussion over allowing humanitarian imports of fuel into Gaza.

This is a developing story.