Israeli tanks pushed into northern parts of the Khan Younis area in the south of the Gaza Strip on Wednesday and Palestinian medics said Israeli airstrikes had killed at least 20 people across the enclave.
Residents said tanks advanced one day after the Israeli military issued new evacuation orders, saying there had been rocket launches from the area.
With shells falling near residential areas, families left leave their homes and headed westwards towards the humanitarian-designated area of Al-Mawasi nearby.
Medics said 11 people were killed in three airstrikes on areas in central Gaza, including six children and one medic. Five of the dead had been queuing outside a bakery, they said.
A further nine Palestinians were killed by tank fire in Rafah, near the border with Egypt, medics said.
Israel's military did not immediately comment on the medics' reports.
Israeli forces fired on the Kamal Adwan Hospital in Beit Lahiya in northern Gaza for the fifth successive day, hospital director Hussam Abu Safiya said, adding that three of his medical staff had been wounded, one critically, on Tuesday night.
Residents in three towns - Jabalia, Beit Lahiya and Beit Hanoun - said Israeli forces had blown up dozens of houses.
Palestinians say Israel's army is trying to drive people out of the northern edge of Gaza with forced evacuations and bombardments to create a buffer zone.
The Israeli army denies this and says it has returned to prevent Hamas fighters from regrouping in an area where it had previously cleared them out.
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