US President Barack Obama has backed Israeli's right to self-defence, but warned against escalation in Gaza.
Speaking to Prime Minister Benjamin Netanyahu on Friday, he underlined his support for Israel's right to defend itself against Palestinian militants.
But he said he was "deeply concerned" about civilian losses, with the Palestinian death toll now over 300.
UN Secretary General Ban Ki Moon will arrive in the region on Saturday to try to mediate between Israel and Hamas.
Ban's visit would aim to help Israelis and Palestinians "end the violence and find a way forward", UN political affairs chief Jeffrey Feltman said.
"Israel has legitimate security concerns, and we condemn the indiscriminate rocket fire from Gaza into Israel. But we are alarmed by Israel's heavy response," Feltman added.
Israel's ground operation followed 10 days of airstrikes on Gaza, which failed to stop Hamas firing rockets across the border.
Meanwhile, Palestinian President Mahmoud Abbas has asked Turkey and Qatar to urge Hamas to accept the terms of an Egyptian-brokered ceasefire with Israel.
At least 60 Palestinians are thought to have been killed since Israel launched the ground offensive in Gaza on Thursday.
More than 300 Palestinians - three-quarters of them civilians - have been killed since the start of the wider Israeli operation on 8 July, according to officials in Gaza.
One Israeli soldier and one Israeli civilian have been killed in the clashes and several Israelis have been seriously injured.
Netanyahu insisted that the ground operation was necessary to target a Hamas tunnel network, which the Israel military could not do "only from the air".
President Obama said "no nation should accept rockets being fired into its borders" but called on Israel's military to conduct its operation "in a way that minimises civilian casualties."
"The US and our friends and allies are deeply concerned about the risks of further escalation and the loss of more innocent life," he told reporters at the White House.
UN officials say more than 40,000 Palestinians have sought shelter from Israel's ground offensive.
After a relative lull in clashes on Friday, there were reports of increased Israeli tank fire overnight and further airstrikes early on Saturday morning.