In Beijing, Egyptian President Abdel Fattah al-Sisi called for increased humanitarian aid to Gaza, and reiterated his country's opposition to “any attempt to force Palestinians to flee their land”.
His host, Chinese leader Xi Jinping, called for a “broad-based, authoritative and effective international peace conference” to tackle the war.
Hamas later said it had told mediators it would agree to a “comprehensive” ceasefire deal, including a hostage-prisoner swap, only if Israel halted its “aggression.”
Witnesses in Gaza said fighting took place in central and western Rafah and bombing in the east left at least five people dead near an aid depot.
Images obtained by AFP from the Al-Aqsa Martyrs Hospital in central Deir al-Balah showed malnourished children waiting for treatment.
The United Nations has warned of famine in Gaza. This weekend Israel said it had stepped up aid deliveries, including through the Kerem Shalom crossing into Gaza.
Witnesses reported that Israeli forces demolished buildings in eastern Rafah, where the Israeli offensive began on May 7. Initially their focus was on the important Rafah border crossing, a major entry point for aid.
On Thursday, Israel said its forces had killed nearly 300 Palestinian militants in Rafah since launching an operation in the city.
Masses of civilians fled Rafah, carrying their belongings on their shoulders, in cars, or on carts pulled by donkeys.