The Palestine Red Crescent Society (PRCS) charity says the Gazan city of Rafah has come under "violent" attack, with a number of deaths reported.
Witnesses spoke of dozens of air strikes on the city's north and centre.
The Israeli military said it had conducted a strikes in southern Gaza, without giving further details.
It follows warnings from the international community over Israel's planned offensive in the city, where 1.5 million people are sheltering.
The United Nations has said there is nowhere safe to go for the Palestinians who have ended up in the far south of the Palestinian territory.
On Sunday, US President Joe Biden told Israel's prime minister a military operation in Rafah should not happen without measures to ensure the safety of civilians.
Israel-Gaza war: 'Violent' strikes reported in Gazan city of Rafah