LONDON -- The "specter of death" is hanging over Gaza amid an impasse over humanitarian access into the blockaded strip and Israel's "total siege" of Gaza, which has cut off the supply of water, food and fuel, U.N. Emergency Relief chief Martin Griffiths warned.

Humanitarian aid and relief convoys carrying "hundreds of tonnes" of essential items have been streaming towards Egypt's Sinai Peninsula, his organization said. Many have parked outside Gaza awaiting access to the besieged enclave as pressure mounts for establishment of a humanitarian corridor that would enable the urgent delivery of aid.

"Aid access is our overwhelming priority," Griffiths said. "And we are in deep discussions hourly with the Israelis, with the Egyptians, with the Gazans about how to do that."

Speaking Tuesday ahead of President Joe Biden's expected Wednesday trip to the region, U.S. Secretary of State Antony Blinken said it is "critical" that aid begins flowing into Gaza.

He announced that the United States and Israel have "agreed to develop a plan that will enable humanitarian aid from donor nations and multilateral organizations to reach civilians in Gaza."

However, Egyptian authorities have said that Israel is not cooperating with delivery of aid into Gaza, with Egypt's Foreign Minister Sameh Shoukry telling reporters that talks are yet to be fruitful, rendering the Rafah crossing -- the sole remaining official exit out of Gaza -- out of use.

"Until now the Israeli government has not taken a position on opening the Rafah crossing from the Gaza side to allow the entrance of assistance and exit of citizens of third countries," said Shoukry.

At least four Israeli airstrikes have been recorded near the Rafah border crossing since the war began.

Medical Aid for Palestinians told ABC News that the humanitarian crisis in Gaza is deepening, with local health services "overwhelmed."

"For more than 16 years, Gaza has been suffering from an illegal blockade weakening it day by day. Medicines and drugs, before this escalation, were at 48% and 29% shortages. Health staff have always been overwhelmed and never paid enough, and lack of specialists was always an issue," said Mahmoud Shalabi, Senior Programmes Manager for Medical Aid for Palestinians in Gaza. "Now, the situation is even worse, and worse than any other escalation that Gaza has gone through"

As the conflict enters day 11, at least 4,178 lives have been lost, including at least 1,400 killed in Israel and at least 2,778 in Gaza, according to the Israeli Health Ministry and the Palestinian Health Ministry.

"One healthcare worker described to me the situation at Gaza's largest emergency department as a slaughterhouse with bodies on the ground and no space to deal with huge influx of injuries," said Shalabi.

"Right now, Gaza needs medicines, medical disposables, and equipment. In addition, health staff and humanitarians need safe corridors to reach people and conduct their work safely without being targeted. The IDPs need shelter, food, health, psychosocial services, water, and the list goes on," said Shalabi.

"We hope that we will come out of this alive."

Food and water supplies are also dwindling, aid organizations warning there are just "days" of stocks left for Gazans: "There is not one drop of water, not one grain of wheat, not a liter of fuel that has been allowed into the Gaza Strip for the last eight days," said Philippe Lazzarini, chief of U.N. Aid for Palestinians.

The World Health Organization has said it is "advocating vigorously for the opening of Rafah crossing."

"Not just one-time access but sustained, unhindered access to Gaza," said WHO's Regional Emergency Director Dr. Richard Brennan.

The organisation has raised concerns over potential disease outbreaks with at least 400,000 internally displaced persons seeking shelters in UNRWA schools. Overcrowding, lack of clean water and sanitation could lead to the spread of infections like cholera and dysentery, compounding on the plight of Gazans.

Biden is on Wednesday due to head to Israel and Jordan, expected to discuss "humanitarian needs of civilians in Gaza" with Jordan's King Abdullah, Egyptian President Abdel Fattah El-Sisi and Palestinian Authority President Mahmoud Abbas.

"The siege in Gaza, the way it is imposed, is nothing else than collective punishment," said Lazzarini. "So, before it is too late, the siege must be lifted and aid agencies must be able to safely bring in essential supplies such as fuel, water, food and medicine."