The Palestinian Red Crescent Society reported three displaced individuals killed and two wounded at its headquarters in Khan Younis.
Gaza health ministry accused Israel of targeting Nasser Hospital, hindering access for medics and patients.
Israel claims Hamas operates near hospitals, a charge denied by hospital staff and Hamas.
UN coordinator Martin Griffiths mentioned 24 people killed in strikes on aid facilities in Khan Younis.
The World Health Organization delivered fuel to Al-Shifa Hospital, while UN Secretary-General Antonio Guterres condemned the destruction in Gaza.
Diplomacy for a ceasefire is ongoing, with Qatar expressing optimism and U.S. envoy Brett McGurk holding discussions in Cairo.
The situation remains complex amid blame for the collapse of a previous truce.
