Israeli forces besieged Al-Amal and Nasser hospitals in the southern city of Khan Younis in Gaza on Sunday, pinning down medical teams under heavy gunfire, the Palestinian Red Crescent said.
They said one of its staff was killed when Israeli tanks suddenly pushed back into areas around the two hospitals, amid heavy bombardment and gunfire.
Israeli armoured forces sealed off Al-Amal Hospital and carried out extensive bulldozing operations in its vicinity, the Red Crescent said in a statement, adding: "All of our teams are in extreme danger at the moment and are completely immobilised."
It said Israeli forces were now demanding the complete evacuation of staff, patients and displaced people from Al Amal's premises and were firing smoke bombs into the area to force out its occupants.
The Israeli military said its forces were hitting "infrastructure" in Khan Younis used as gathering points for many militants. Hamas denies using hospitals for military ends and accuses Israel of war crimes against civilian targets.
The health ministry in Hamas-run Gaza said dozens of patients and medical staffers had been detained by Israeli forces at Al Shifa in Gaza City in the enclave's north that has been under Israeli control for a week.
Al Shifa is one of the few healthcare facilities even partially operational in north Gaza, and - like others - had also been housing some of the nearly 2 million civilians - over 80 per cent of Gaza's population - displaced by the war.
Reuters has been unable to access Gaza's contested hospital areas and verify accounts by either side.
Khan Younis residents said Israeli tanks also advanced in a western neighbourhood near Nasser Hospital under cover of heavy fire from the air and ground.
In Rafah, Gaza's southernmost town on the Egyptian border town that has become the last refuge for half of Gaza's uprooted population, an Israeli air strike on a house killed seven people, health officials said.
At least 32,226 Palestinians have been killed and 74,518 injured in Israel's air and ground offensive into the densely populated coastal territory since October 7, its health ministry said in a Sunday update.
Concerted mediation by Qatar and Egypt, backed by the United States has so far failed to secure a Hamas-Israel ceasefire, prisoner releases and unfettered aid to Gaza civilians facing famine, with each sides sticking to core demands.
Hamas wants any truce deal to include an Israeli commitment to end the war and withdraw forces from Gaza. Israel has ruled this out, saying it will keep fighting until Hamas is eradicated as a political and military force.