US President Joe Biden has told Israel's Prime Minister Benjamin Netanyahu he expects a "significant de-escalation" in the Gaza conflict on Wednesday.
Biden wanted a "path to ceasefire", the White House said.
The US is a staunch ally of Israel and has so far opposed a joint UN Security Council statement on the conflict.
In response Netanyahu said he was "determined to carry on" until "calm and security are restored to Israeli citizens", according to Israeli media.
The conflict is in its 10th day, with a continuing exchange of rocket fire from Palestinian militants into Israel and Israeli air strikes on Gaza.
On Wednesday, four rockets were also fired from Lebanon into Israel and Israel's military responded by firing artillery shells at "a number of targets in Lebanese territory". It was not immediately clear whether this would prove to be a significant escalation.
The Gaza fighting began after weeks of rising Israeli-Palestinian tension in occupied East Jerusalem that culminated in clashes at a holy site revered by both Muslims and Jews. Hamas, which controls Gaza, began firing rockets after warning Israel to withdraw from the site, triggering retaliatory air strikes.
At least 219 people, including almost 100 women and children, have been killed in Gaza so far, according to its health ministry. Israel has said at least 150 militants are among those killed in Gaza. Hamas does not give casualty figures for fighters.
In Israel 12 people, including two children, have been killed, its medical service says. Israel says some 3750 rockets have been fired towards its territory by militants in Gaza.