One of the three hospitals in Rafah, Al-Najjar, is no longer functioning due to the ongoing hostilities in its vicinity and Israel's military operation, according to the World Health Organization.

"Hospitals in the south of Gaza only have three days of fuel left, which means services may soon come to a halt," the WHO warned.

The closure of the border crossing continues to prevent the entry of fuel needed for aid operations; without fuel all humanitarian operations will stop, the WHO warned. Border closures are also impeding delivery of humanitarian aid into Gaza, the WHO said.

"At a time when fragile humanitarian operations urgently require expansion, the Rafah military operation is further limiting our ability to reach thousands of people who have been living in dire conditions without adequate food, sanitation, health services and security. This must stop now," the WHO said.

-ABC News' Will Gretsky

Israel said it has reopened the Kerem Shalom Crossing Wednesday for the entry of humanitarian aid into the Gaza Strip.

"Trucks from Egypt carrying humanitarian aid, including food, water, shelter equipment, medicine, and medical equipment donated by the international community are already arriving at the crossing. After a thorough security inspection by the security personnel of the Ministry of Defense Crossing Authority, the equipment will be transferred to the Gazan side of the crossing," Israel said in a statement.

Israel had closed the crossing after it said Hamas fired a rocket toward the area over the weekend, killing four Israeli soldiers.

-ABC News' Will Gretsky

Thirty people, including six children and eight women, have been killed and 146 others were injured in Rafah on Tuesday, a spokesperson for Al Kuwaiti hospital in Rafah told ABC News.

People in at least six neighborhoods have started evacuating in eastern Rafah.

"With more than 1.5 million civilians crowded into this sliver of land, an Israeli military escalation threatens to turn Rafah into a graveyard. We are calling for an immediate and sustained ceasefire to prevent more civilian deaths and injuries in Gaza and enable the urgent scale-up of humanitarian aid. The survival of civilians in Gaza depends on it," Avril Benoît, executive director of Doctors Without Borders USA.

Aid groups, including the International Rescue Committee, have called on Israel to halt its ground incursion in Rafah and across Gaza, warning that civilians have no place to go.

"The dire warnings of aid groups have materialized: Israeli forces have launched a ground incursion into eastern Rafah and have taken control of the Palestinian side of the border crossing. Over a million civilians are now in imminent danger and aid flow through the Rafah crossing has halted with no aid trucks entering since May 5," said Bob Kitchen, IRC vice president of emergencies.

"Already, dozens of civilians are reported to have been killed in overnight Israeli airstrikes on Rafah City, while hundreds of thousands more remain at grave risk from the threat of further conflict and a lack of access to life-saving assistance. It is unconscionable to target such a densely populated area, leaving 1.3 million people with no safe haven," Kitchen said.

-ABC News' Ellie Kaufman and Will Gretsky

The White House expects the Kerem Shalom crossing to reopen on Wednesday, but are working to move up that timeline to get vital humanitarian assistance into northern Gaza even sooner.

“Israel has committed to reopening the Kerem Shalom,” White House press secretary Karine Jean-Pierre told ABC News. “We've been told that that's going to happen tomorrow. We are working to move that up.”

“Fuel deliveries through Rafah should also commence tomorrow. That's what we've been told. And we believe Rafah border crossing should also be quickly reopened for the movement of humanitarian assistance. We are insisting that there should be no disruptions of humanitarian assistance flows," Jean-Pierre said.

Jean-Pierre would not say if the U.S. still expects the Israelis to alert them when they do plan to go ahead with a full-scale operation in Rafah, but reiterated that they do not support the IDF carrying that out.

"We do not want to see a major operation happening in Rafah. We want to see a plan, a comprehensive plan, on how Israel plans to protect the 1.5, more than 1 million civilians that are currently seeking refuge in Rafah," Jean-Pierre said.

-ABC News' Mary Bruce and Justin Gomez