The United States continued to push for a cease-fire in Gaza Tuesday as Secretary of State Antony Blinken met Egyptian leaders in Cairo.

Blinken's visit also comes amid growing concerns in Egypt about Israel's stated intentions to expand the combat in Gaza to areas on the Egyptian border that are crammed with displaced Palestinians.

Israel's Defense Minister has said Israel's offensive will eventually reach the town of Rafah, on the Egyptian border, where more than half of Gaza's 2.3 million people have sought refuge and are now living in increasingly miserable conditions.

U.N. humanitarian monitors said Tuesday that Israeli evacuation orders now cover two-thirds of Gaza's territory, driving thousands more people every day toward the border areas.

Egypt has warned that an Israeli deployment along the border would threaten the peace treaty the two countries signed over four decades ago. Egypt fears an expansion of combat to the Rafah area could push terrified Palestinian civilians across the border, a scenario Egypt has said it is determined to prevent.

Blinken, who met Tuesday with Egyptian President Abdel-Fattah el-Sissi, has said repeatedly that Palestinians must not be forced out of Gaza.

During his latest trip, Blinken is seeking progress on a cease-fire deal, on potential normalization of relations between Israel and Saudi Arabia, and on preventing an escalation of regional fighting.

On all three fronts, Blinken faces major challenges. Hamas and Israel are publicly at odds over key elements of a potential truce. Israel has dismissed the United States' calls for a path to a Palestinian state, and Iran's militant allies in the region have shown little sign of being deterred by U.S. strikes.

Egypt – along with Qatar, where Blinken will be later Tuesday – have been trying to mediate an agreement between Israel and Hamas that would lead to the release of more hostages in return for a several-weeklong pause in Israeli military operations.

The outlines of such a deal were worked out by intelligence chiefs from the U.S., Egypt, Qatar and Israel late last month and have been presented to Hamas, which has not yet formally responded.

U.S. officials said Blinken is hoping to get an update on the Hamas response to the proposal in both Cairo and Doha. Blinken will then travel to Israel to brief Israeli Prime Minister Benjamin Netanyahu and his War Cabinet on Wednesday about what he heard from the Arab leaders.

As on his previous four trips to the Mideast since the Gaza war began, Blinken's other main goal is to prevent the conflict from spreading, a task made exponentially more difficult by stepped-up attacks by Iran-backed militias in the region and increasingly severe U.S. military responses in Iraq, Syria, Yemen and the Red Sea that have intensified since last week.

Blinken met with Crown Prince Mohammed bin Salman on Monday evening, shortly after arriving in the Saudi capital, Riyadh. Saudi officials have said the kingdom is still interested in normalizing relations with Israel in a potentially historic deal, but only if there is a credible plan to create a Palestinian state.

Blinken "underscored the importance of addressing humanitarian needs in Gaza and preventing further spread of the conflict," and he and the crown prince discussed "the importance of building a more integrated and prosperous region," the State Department said in a statement.

Any such grand bargain appears a long way off as the war still rages in Gaza.

The Palestinian death toll from nearly four months of war has reached 27,585 according to the Gazan Health Ministry, with the bodies of 107 people brought to hospitals over the past day.

The war has leveled vast swaths of the tiny enclave and pushed a quarter of residents to starvation.

Israel has vowed to continue the war until it crushes Hamas' military and governing abilities and wins the return of the 100-plus hostages still held by the Palestinian resistance group.

The Oct. 7 incursion killed some 1,140 people and abducted around 250 people, igniting the war. More than 100 captives, mostly women and children, were released during a weeklong cease-fire in November in exchange for the release of 240 Palestinians imprisoned by Israel.

The Israeli military said Tuesday it was battling resistance groups in areas across the Gaza Strip, including the southern city of Khan Younis, where it said troops killed dozens of members over the past day.

An Israeli airstrike in the city hit an apartment building, killing two parents and four of their five children, according to the children's grandfather.

Mahmoud al-Khatib said his 41-year-old son, Tariq, was sleeping along with his family when an Israeli warplane bombed their apartment in the middle of the night.

U.N. humanitarian monitors said Tuesday that Israel's evacuation orders in the Gaza Strip now cover two-thirds of the territory, or 246 square kilometers (95 square miles). The affected area was home to 1.78 million Palestinians, or 77% of Gaza's population, before the war.

The U.N. Office for the Coordination of Humanitarian Affairs, or OCHA, said in its daily report that the newly displaced only have about 1.5-2 liters (50-67 ounces) of water per day to drink, cook and wash. It also reported a significant increase in chronic diarrhea among children.

Parents of babies face a particularly difficult challenge because of the high cost or lack of diapers, baby formula and milk.

Zainab al-Zein, who is sheltering in the central town of Deir al-Balah, said she had to feed her 2.5-month-old daughter solid food, such as biscuits and ground rice, well ahead of the typical 6-month mark because milk and formula were not available.

⁠"This is known, of course, as unhealthy eating, and we know that it causes her intestinal distress, bloating and colic," al-Zein said. "As you can see, 24 hours like this, she cries and cries continuously."