More than 30 members of two Palestinian families have been killed by Israeli strikes, health officials in Gaza say.
The overnight strikes in southern Gaza came as the Palestinian death toll from the two-week conflict passed 500.
Meanwhile, Hamas launched fresh rocket attacks and used tunnels out of Gaza to infiltrate Israel near the town of Sderot, where 10 militants were killed.
Twenty Israelis - 18 of them soldiers - have died, Israel says, as it seeks to end rocket fire from Gaza.
In Egypt, US Secretary of State John Kerry is due to hold talks aimed at securing a ceasefire.
The UN Security Council has issued a call for an "immediate cessation of hostilities", but did not endorse a strongly worded draft resolution backed by Arab states.
UN Secretary General Ban Ki-moon has criticised an Israeli operation in the densely populated area of Shejaiya on Sunday as "an atrocious action".
At least 67 people were reported killed in the assault on Shejaiya, which Israel said was a "terror stronghold".
Violence continued on Monday in the wake of a deadly Sunday in which 13 Israeli soldiers and more than 100 Palestinians lost their lives.
Israel says it has killed at least 120 militants since the ground offensive began on Thursday night.
Palestinian emergency services spokesman Ashraf al-Qudra said nine members of one family were killed in Israeli attacks on Rafah, on the border with Egypt.
In Khan Younis, in the south of Gaza, at least 23 members of one family died when a building was hit by an Israeli air strike, officials said.
"Doesn't this indicate that Israel is ruthless? Are we the liars?" family member Sabri Abu Jamea told AP.
"The evidence is here in the morgue refrigerators."
Further north, Israel continued its ground operation in the eastern fringes of Gaza City.
After moving into the Shejaiya neighbourhood on Sunday in search of rocket sites and tunnels, nearby areas were pounded with artillery on Monday morning.
The BBC's Paul Adams, at the scene, reports that more than 83,000 people across Gaza have taken refuge in schools run by the UN.
Sunday's operation in Shejaiya prompted chaotic scenes, with thousands of residents fleeing and images of children being pulled from the wreckage of buildings.
Israel sent ground troops into Gaza after days of heavy air and naval barrages failed to stop rocket fire.
Israel says the ground operation is necessary to target Hamas' network of tunnels, which it says have been used by militants to infiltrate Israel and carry out attacks.
But the UN, Palestinians and Arab states have expressed alarm at the number of civilian casualties.