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.
Mr 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,” Mr Feltman added.
Mr Netanyahu has warned of a “significant expansion” of the offensive but Hamas, the Palestinian group that controls Gaza, said Israel would “pay a high price” for the invasion.
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.