CAIRO/GAZA/JERUSALEM - The talks held with the Israeli negotiators in Egypt on Tuesday for a truce with Hamas were "positive" and could lead to an imminent end of the current Israeli military operation in the southernmost Gazan city of Rafah, Egyptian sources told Xinhua on condition of anonymity.

"Today's meeting with the Israeli delegation addressed some of the six points of disagreement between Israel and Hamas and made progress in the discussions," the sources added.

Among the points of disagreement between Israel and Gaza-ruling Hamas is that Israel seeks the release of three Israeli hostages every three days, while Hamas agrees to release three every week.

The two sides also failed to reach a consensus on Hamas's request to release a list of Palestinians, the sources said.

Israeli Defense Minister Yoav Gallant warned that if the ongoing ceasefire negotiations in Cairo fail, Israel will escalate its military assault on Rafah

Israel doesn't want Hamas to control the Palestinian side of the Rafah border crossing and the negotiating sides are discussing a different Palestinian body, according to the sources.

READ MORE: Hamas calls for US, global pressure to stop escalation in Rafah

Earlier on Tuesday, Egypt hosted delegations from Hamas, Israel, Qatar, and the United States to reach a comprehensive truce in Gaza.

In a video statement, Israeli Prime Minister Benjamin Netanyahu said he had instructed the delegation to "continue to stand firm on the conditions necessary for the release of our hostages, continue to stand firm on the essential requirements to ensure Israel's security".

He noted that the ceasefire proposal, brokered by Egyptian and Qatari mediators and approved by Hamas on Monday, fell short of Israel's essential requirements.

Israeli Defense Minister Yoav Gallant warned that if the ongoing ceasefire negotiations in Cairo fail, Israel will escalate its military assault on Rafah.

He said that Israel "is ready for compromise in order to bring the hostages back home". However, he added that if no progress is made, "we will deepen the operation throughout the Gaza Strip".

ALSO READ: Report: At least 20 killed as Israeli army pounds Rafah

Benny Gantz, a member of Israel's wartime Cabinet, also emphasized the urgency of reaching a deal. "The delegation not only has the mandate to listen but also the obligation to act for an agreement to free the hostages," he stated.

Ongoing attacks on Gaza

Gallant's warning came hours after Israeli tanks and warplanes stormed Rafah, where about 1.4 million displaced people have sought refuge from bombardments elsewhere, according to estimates by the United Nations.

The Israeli army wrote on social media platform X that four mortar shells and two rockets were launched from Rafah toward Israeli territory, triggering sirens in the Kerem Shalom area

Residents reported heavy bombardments. According to the Palestinian official news agency WAFA, at least 20 Palestinians were killed. The Israeli army said that those killed were militants.

READ MORE: Israel launches airstrikes on eastern Rafah, Hamas 'mulls halting talks'

Meanwhile, the Israeli army wrote on social media platform X that four mortar shells and two rockets were launched from Rafah toward Israeli territory, triggering sirens in the Kerem Shalom area. However, no injuries or damages were reported.

The Israeli army announced on Tuesday it had attained "operational" control over the Palestinian side of the Rafah Crossing, following what it described as a "precise counter-terrorism operation" in the eastern area of Rafah during the night.

Video footage circulating on social media, recorded by soldiers, showed the raising of the Israeli flag near the Rafah Crossing. The area appeared deserted, following Israel's warning to civilians in the densely populated eastern Rafah to evacuate to tents in Al Mawasi and Khan Younis.

The General Authority for Borders and Crossings in Gaza said in a brief statement that operations at the Rafah land crossing were suspended following the entry of Israeli tanks into the crossing facilities from Palestinian territory.

READ MORE: Blinken tells Netanyahu US opposes Rafah ground attack plan

Passenger movement from Gaza has ceased, and the entry of humanitarian and relief aid into the enclave has been halted, it added.

Algeria, Lebanon, Jordan and Iran on Tuesday condemned the Israeli military operations in Rafah.

Health authorities in Gaza on Tuesday said the Palestinian death toll from ongoing Israeli attacks has risen to 34,789

The United Nations Relief and Works Agency for Palestine Refugees (UNRWA) on Tuesday warned of disruptions in aid delivery and fuel supplies to the Gaza Strip via the Rafah crossing bordering Egypt.

ALSO READ: UN warns of surge in casualties from potential Gaza escalation

Israel launched a large-scale offensive against Hamas in the Gaza Strip to retaliate the movement's surprise attack on southern Israel on Oct 7, 2023, during which about 1,200 people in Israel were killed and more than 200 were taken hostage.

Health authorities in Gaza on Tuesday said the Palestinian death toll from ongoing Israeli attacks has risen to 34,789.

The Israeli army killed 54 people and wounded 96 others during the past 24 hours, bringing the total death toll to 34,789 and injuries to 78,204 since the conflict broke out, the authorities said in a statement.

At least one Palestinian was killed and nine others were injured by Israeli troops' gunfire during a nearly 20-hour military operation in the city of Tulkarm in the northern West Bank, Palestinian medical sources said on Tuesday.

UN chief urges ceasefire

As tensions continue to escalate in Gaza, UN Secretary-General Antonio Guterres on Tuesday once again called for Israel and Hamas to demonstrate "political courage" and work towards securing a ceasefire.

Speaking to reporters at UN headquarters in New York, Guterres highlighted the critical situation in the Gaza Strip, especially in Rafah.

Even the best friends of Israel are clear: An assault on Rafah would be a strategic mistake, a political calamity, and a humanitarian nightmare.

Antonio Guterres, UN Secretary-General

Guterres expressed concern about the humanitarian situation, noting that essential aid and fuel supplies are nearly depleted. "The closure of both the Rafah and Karem Shalom crossings is especially damaging to an already dire humanitarian situation. They must be re-opened immediately," he stated.

ALSO READ: China: US’ veto on Palestine doesn't match role of responsible power

With over 1,100 Israelis and 34,000 Palestinians reported killed due to recent conflicts, Guterres emphasized the staggering cost of the ongoing violence. "Haven't we seen enough?" he implored, stressing the immediate need for both sides to engage in diplomacy rather than further escalation.

The UN chief underscored the severe consequences of continued fighting, particularly any potential full-scale assault on Rafah, which he described as a looming "human catastrophe". He warned, "Countless more civilian casualties. Countless more families forced to flee yet again -- with nowhere safe to go. Because there is no safe place in Gaza."

ALSO READ: UN report warns of human development in Gaza being wiped out

Guterres's remarks reflect deep concern about the impact of the conflict not only on Gaza but also on the broader Middle East. "Even the best friends of Israel are clear: An assault on Rafah would be a strategic mistake, a political calamity, and a humanitarian nightmare," he said, calling on those with influence over Israel to help avert further tragedy.