The Rafah border crossing between Egypt and Gaza remained closed on Wednesday, Israel said, as the delicate ceasefire between Israel and Hamas continued to take hold.

"The defense establishment clarifies that, contrary to reports, the Rafah Crossing did not open today," an Israeli security official told ABC News. "Preparations are ongoing for its opening for the exit and entry of Gazans only."

Aid for Palestinians in the enclave is traveling through other crossings, including the Kerem Shalom crossing, the official said. Israeli security forces are inspecting aid before it enters the strip, the official said.

International aid groups, including the U.N.'s agency for Palestinian refugees, have urged Israel to let more aid into Gaza.

"We have enough food for the entire population for 3 months waiting in Egypt and Jordan," UNWRA said in a statement on Tuesday. "There’s no more time to lose -- we need a green light to start bringing in UNRWA’s supplies immediately so our teams can deliver them to people in need."

-ABC News' Jordana Miller and Kevin Shalvey

The United Nations' World Food Programme said it is "scaling up its operations in Gaza" as the ceasefire has gone into effect.

Since Saturday, 137 trucks with food aid have gone into Gaza "to support bakeries, nutrition programmes and general food distributions," the organization said in a release Tuesday.

"With full access, WFP intends to restore its regular food distribution system, scaling assistance through 145 distribution points across the Strip," the organization said.

-ABC News' Ellie Kaufman

The remains of four more hostages have been handed over to Israel.

Four coffins of deceased hostages, escorted by Israeli forces, crossed the border into Israel, headed to the National Institute for Forensic Medicine, where officials will carry out identification procedures.

There are still believed to be 20 hostage bodies remaining in Gaza.

The United Nations and other aid organizations “have been able to move more freely across parts of Gaza from which Israeli forces have withdrawn,” since the first phase of the ceasefire deal went into effect, U.N. Deputy spokesperson for the Secretary General Farhan Haq said at a press briefing at U.N. headquarters in New York Tuesday.

"This improved access has allowed partners to scale up the response to the most urgent needs," Haq said.

World Health Organization teams reached Al Ahli Hospital with eight trucks of medical supplies on Monday, and their teams reached the European Hospital in Khan Younis to transfer critical medications and intensive care unit equipment to Nasser Hospital, Haq said.

"The U.N. and our humanitarian partners have also installed a solar panel for a desalination unit in Deir al Balah, as well as new telecommunications hardware to improve connectivity for affected people and humanitarian operations," Haq said.