RAFAH, Gaza Strip — The opening today of the border crossing between Egypt and Gaza will let a trickle of aid into the besieged district for the first time since Israel sealed it off following Hamas’ bloody rampage two weeks ago.

Just 20 trucks were allowed in to start, and more than 200 trucks carrying roughly 3,000 tons of aid have been positioned near the crossing for days. Gaza’s 2.3 million Palestinians Arabs, half of whom have fled their homes, are rationing food and drinking dirty water.

Hospitals, many of them under the Hamas-controlled health authorities, say they are running low on medical supplies and fuel for emergency generators amid a territory-wide power blackout. Israel is launching waves of airstrikes across Gaza, as Palestinian militants fire rocket barrages into Israel.

The opening came after more than a week of high-level diplomacy by various mediators, including visits to the region by President Biden and Secretary-General Guterres of the United Nations. Israel had insisted that nothing would enter Gaza until Hamas released all of the captives from its October 7 attack on towns in southern Israel.

Late Friday, Hamas released an American woman and her teenage daughter, the first captives to be freed. It was not immediately clear if there was a connection between the release and the aid deliveries. Israel says Hamas is still holding at least 210 captives.

On Saturday morning, an Associated Press reporter on the Palestinian side of Rafah saw the 20 trucks heading north to Deir al-Balah, a quiet farming town where many evacuees from the north have sought shelter. Hundreds of foreign passport holders at Rafah and hoping to escape the conflict were not allowed to leave.

The trucks were carrying 44,000 bottles of drinking water from the U.N.’s children’s agency — enough for 22,000 people for a single day, it said. “This first, limited water will save lives, but the needs are immediate and immense,” said the director, Catherine Russell, of the United Nations Children’s Fund.

The World Health Organization said four of the 20 trucks that crossed through Rafah were carrying medical supplies, including essential supplies for 300,000 people for three months, trauma medicine and supplies for 1,200 people, and 235 portable trauma bags for first responders.

“The situation is catastrophic in Gaza,” the head of the UN’s World Food Program, Cindy McCain, told the AP. “We need many, many, many more trucks and a continual flow of aid,” she said, adding that some 400 trucks were entering Gaza daily before the war.

The government in Gaza also said the limited convoy “will not be able to change the humanitarian catastrophe,” calling for a secure corridor operating around the clock. The Gaza government is run by Hamas, which intentionally launched a slaughter of Israeli civilians on October 7 and with the consequences of which Hamas is now dealing. 

Rear Admiral Daniel Hagari, an Israeli military spokesman, said “the humanitarian situation in Gaza is under control.” He said the aid would be delivered only to southern Gaza, where the army has ordered people to relocate, adding that no fuel would enter the territory.

Secretary Blinken appealed to all sides to keep the crossing open for crucial aid shipments and warned Hamas to not take the aid. “Palestinian civilians are not responsible for Hamas’s horrific terrorism, and they should not be made to suffer for its depraved acts,” he said in a statement.

“As President Biden stated,” Mr. Blinken said, “if Hamas steals or diverts this assistance it will have demonstrated once again that it has no regard for the welfare of the Palestinian people.’’ It will also make it hard to keep the aid flowing, he said.

One Egyptian official said that discussions were taking place on, among other things, the release of dual-national hostages in return for the fuel, but that Israel was insisting on the release of all hostages.

Hamas released Judith Raanan and her 17-year-old daughter, Natalie, on Friday for what it said were humanitarian reasons in an agreement with Qatar, a Persian Gulf nation that has often served as a Mideast mediator. A representative for the pair said they were staying with relatives in central Israel.

The two had been on a trip from their home in suburban Chicago to Israel to celebrate Jewish holidays, the family said. They were in the kibbutz of Nahal Oz, near Gaza, when Hamas and other militants stormed into southern Israeli towns, killing hundreds and abducting at least 210 others.

There are growing expectations of a ground offensive that Israel says would be aimed at rooting out Hamas, an Islamic terrorist organization that has ruled Gaza for 16 years. Israel said Friday it does not plan to take long-term control over the small but densely populated Gaza territory.

Israel has also traded fire along its northern border with the Iran-controlled Hezbollah terrorist organization, raising concerns about a second front opening up. The Israeli military said Saturday it struck Hezbollah targets in Lebanon in response to recent rocket launches and attacks with anti-tank missiles.

“Hezbollah has decided to participate in the fighting, and we are exacting a heavy price for this,” Israel’s defense minister, Yoav Gallant, said during a visit to the border. Israel issued a travel warning on Saturday, ordering its citizens to leave Egypt and Jordan — which made peace with the Jewish state decades ago.

Israel also ordered its citizens to avoid travel to a number of Arab and Muslim countries, including the United Arab Emirates, Morocco, and Bahrain, which forged diplomatic ties with Israel in 2020. Protests against Israel’s actions in Gaza have erupted across the region.

An Israeli ground assault would likely lead to a dramatic escalation in casualties on both sides in urban fighting. More than 1,400 people in Israel have been killed in the war — mostly civilians slain by Hamas.

More than 4,300 people have been killed in Gaza, according to the Hamas-run Health Ministry. That includes the toll from, from among other sources, a hospital explosion. The attack on which, Israel and America have concluded, was launched by Islamic Jihad from inside the Gaza Strip.

Hosting a summit Saturday in Egypt, President el-Sissi called for ensuring aid to Gaza, negotiating a cease-fire, and resuming talks between Israel and the Palestinian Arabs, which last broke down more than a decade ago.

Mr. el-Sissi also said the conflict would never be resolved “at the expense of Egypt,” referring to fears Israel may try to push Gaza’s population into the Sinai Peninsula.