The UN's top court said it would hand down a much-awaited landmark ruling on Friday in the case against Israel over alleged genocide in Gaza.
Heavy fighting drew near to hospitals in Gaza's Khan Younis on Wednesday after Israel said it had intensified its assault on the city that has become the focus of its war.
The United Nations raised fears about the fate of thousands of internally displaced people sheltering - and now trapped - on the grounds of the hospitals in southern Gaza's biggest city.
"Heavy fighting is reported in proximity to hospitals in Khan Younis, including Al-Aqsa, Nasser and Al-Amal, with reports of Palestinians trying to flee to the southern town of Rafah," the UN humanitarian agency OCHA said.
"No-one can enter or exit (Nasser Hospital) due to ongoing bombardments," OCHA said citing medics who also reported that staff were digging graves on the grounds of the facility "due to the large numbers of fatalities anticipated".
OCHA said about 18,000 people uprooted from their homes were reported to be at Nasser Hospital alone.