However a glimmer of progress has emerged, with President Joe Biden in daily discussions with parties involved in talks to secure the release of those abducted by Hamas in its cross-border rampage into Israel on October 7.
More than 235 people are thought to still be held by the Islamist group in Gaza.
When asked by reporters at the White House on Tuesday what his message to family members of hostages was, he said: "Hang in there, we're coming."
ABC News reports progress had been made on a hostage deal, with a breakthrough possible in the next 48 to 72 hours, it said, citing a senior Israeli source.
White House spokesman John Kirby told reporters on the presidential plane, Air Force One, intelligence confirmed Hamas used tunnels underneath Al-Shifa and other hospitals to conceal military operations and hold hostages.
Israel has made the same claims, which Hamas denies.
"We have information that confirms Hamas is using that particular hospital for a command and control node" and probably to store weapons, Kirby said. "That is a war crime."
Five weeks after Israel swore to destroy Hamas in retaliation for militants' cross-border assault, the fate of Al-Shifa has become a focus of international alarm.
Israeli forces have waged fierce street battles against Hamas fighters over the past 10 days, advanced into the centre of Gaza City and surrounded Al-Shifa, the seaside enclave's biggest hospital.
Kirby said the US intelligence came from a variety of methods.
Hamas said on Telegram it rejected US claims about its use of hospitals and that they "give a green light to the Israeli occupation to commit further brutal massacres targeting hospitals".
Omar Shakir, Israel and Palestine director for Human Rights Watch, said even if Hamas was proven to be using hospitals to conduct military operations, international law required effective warnings be given before attacks.
This meant people there needed a safe place to go and a safe way to get there, Shakir said. "It's very alarming because you have to remember hospitals in Gaza are housing tens of thousands of displaced persons."
Hamas says 650 patients and 5000 to 7000 other civilians are trapped inside Al-Shifa hospital grounds, under constant fire from Israeli snipers and drones.
Amid worsening shortages of fuel, water and supplies, it says 40 patients have died in recent days, including three premature babies whose incubators were knocked out.
Palestinians trapped in the hospital were digging a mass grave on Tuesday to bury patients who died and no plan was in place to evacuate babies despite Israel announcing an offer to send portable incubators, Ashraf Al-Qidra, Gaza's health ministry spokesman, said.
An Israeli officer who oversees co-ordination with Gaza said he had been in contact with Al-Shifa's hospital director and presented a plan to evacuate the babies through a safe corridor, possibly to Egypt.
Qidra said so far no arrangements had been established to carry out any evacuation.
"The occupation is still besieging the hospital and they are firing into the yards from time to time," he said.
Qidra said there were about 100 bodies decomposing inside and no way to get them out.
"We are planning to bury them today in a mass grave inside the Al-Shifa medical complex.
"It is going to be very dangerous as we don't have any cover or protection from the ICRC," he said, referring to the International Committee of the Red Cross.
Israel denies the hospital is under siege and says its forces allow exit routes.
Medics and officials inside deny this and say those trying to leave come under fire.
UN Secretary-General Antonio Guterres was deeply disturbed by the "dramatic loss of life" in the hospitals, his spokesman said.
Medical officials in Hamas-run Gaza say more than 11,000 people are confirmed dead from Israeli strikes, around 40 per cent of them children, and countless others trapped under rubble.
Around two-thirds of Gaza's 2.3 million people have been made homeless.
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