Israel launched strikes on Gaza on Sunday after it expanded an evacuation order for Rafah, with the United Nations warning an outright invasion of the crowded southern city risked an "epic" disaster.
Gaza's civil defence agency said two doctors were killed in the central town of Deir al-Balah, in a central area of the Palestinian territory, while AFP correspondents reported heavy gunfire from Israeli helicopters near Gaza City.
Witnesses said Israel had carried out strikes in Rafah near the crossing with Egypt on Saturday, and AFP images showed smoke rising over the city.
Israeli troops defied international opposition this week and entered eastern areas of the city, effectively shutting a key aid crossing and suspending traffic through another.
Israel expanded an evacuation order for eastern Rafah after saying 300,000 people had fled the city since the army urged people to leave earlier in the week.
Residents piled water tanks, mattresses and other belongings onto vehicles and prepared to flee again.
"We don't know where to go," said Farid Abu Eida, who was preparing to leave Rafah, having already been displaced there from Gaza City.
"There is no place left in Gaza that is safe or not overcrowded... There's nowhere we can go."
Residents were told to go to the "humanitarian zone" of Al-Mawasi, on the coast northwest of Rafah.
Hamas accused Israel of "expanding the incursion into Rafah to include new areas in the centre and the west of the city".
Israeli army spokesman Daniel Hagari said, "We have eliminated dozens of terrorists in eastern Rafah", and the army said troops were fighting "armed terrorists" at the crossing and had found "numerous underground tunnel shafts".
UN chief Antonio Guterres said on Friday that Gaza risked an "epic humanitarian disaster" if Israel launched a full-scale ground operation in Rafah.
Unsafe zones
International outrage mounted at Israel's operations in Rafah.
EU chief Charles Michel said on social media that Rafah civilians were being ordered to "unsafe zones", denouncing it as "unacceptable".
Doctors Without Borders (MSF) said it had started transferring 22 patients from a field hospital in Rafah, saying Israel's operations in the city were "making it impossible to provide lifesaving medical assistance".
Israel's offensive has killed at least 34,971 people in Gaza, mostly women and children, according to the Gaza Health Ministry.