US Secretary of State John Kerry has urged Israel and the Palestinians to take advantage of the Gaza truce to move towards broader negotiations.
Mr Kerry told the BBC the situation could concentrate minds on the need to negotiate a two-state solution.
A 72-hour humanitarian truce is holding in Gaza, halting a four-week conflict that has claimed more than 1,900 lives.
Israel and the Palestinians have sent delegations to Cairo to discuss the possibility of a longer-term truce.
Mr Kerry, in a BBC interview, said the US fully supported Israel's right to defend itself against militant rocket attacks.
"No country can live with that condition and the United States stands squarely behind Israel's right to defend itself in those circumstances. Period."
Mr Kerry said that Hamas, which controls Gaza, had "behaved in an unbelievably shocking manner engaging in this activity and, yes, there has been horrible collateral damage as a result".
Asked whether he supported Palestinian demands for a lifting of Israel's blockade of Gaza, Mr Kerry said: "What we want to do is support the Palestinians in their desire to improve their lives and to get food in and to open crossings and to reconstruct and have greater freedom."
But he said that had to come "with a greater responsibility towards Israel, which means giving up rockets".
Israeli offensive began
4,760+ air strikes on Gaza
3,488 rockets fired at Israel
1,973 people killed in Gaza
UN estimates +70% of deaths are civilians
3 civilians killed in Israel
64 Israeli soldiers killed
Mr Kerry said all this would only come together with a "bigger, broader approach to the underlying solution of two states" that would provide security for Israel and "a better life and greater freedoms for the Palestinians".
Mr Kerry added: "I believe that the situation now that has evolved will concentrate people's minds on the need to get back to the negotiations and try and resolve the issues of the two states."
Tuesday's truce came into effect at 08:00 local time (05:00 GMT) and has so far held.
Israel withdrew all forces to positions outside Gaza and many Gazans began to return to discover the state of their homes following the four-week conflict.
Manar Abu Louli returned to find that her home in Rafah had been used by the Israelis as a makeshift field HQ.
"She is lucky," a relative told Associated Press (AP). "If they had not wanted to use her home for shelter, they would have shelled it to bits."
Some Israelis close to the border were unconvinced the military had finished its job removing tunnels used by militants to infiltrate Israel.
"Who can promise me that all the tunnels have been destroyed? I am angry that they are not pressing on with the offensive," Leah Musafi, who lives on the Nir Am kibbutz, told Reuters.
At the scene: Jon Donnison, Gaza
Hundreds of thousands of displaced Palestinians in Gaza have been returning to their homes. Many have found nothing left.
We met the Za'Noun family in Beit Hanoun, one of the worst affected areas right on the border with Israel. Their family home has been destroyed for the third time.
The Za'Nouns will rebuild again. "Where else can we go?" Khalil Za'Noun, 80, asked me.
One of his 34 grandchildren, Mohammed, has already lived through four wars in his short life. He's just 14.
But this will not be the last war in Gaza. This truce is only a short-term fix. None of the big issues between Israelis and Palestinians has been fixed.
The latest ceasefire was brokered by Egypt in talks between Palestinian delegates in Cairo on Monday.
Israel did not take part but has now sent a team for indirect negotiations.
The main Palestinian demands include the end of Israel's blockade of the territory and the opening of border crossings. They will also want internationally funded reconstruction.
Israeli government spokesman Mark Regev said Israel's main focus for a longer-term deal would be on demilitarising Gaza to achieve a "sustained period of quiet".
But senior Hamas official Izzat Rishq told AP: "We'd take the life of anyone who tries to take the weapons of resistance."
Israel launched Operation Protective Edge on 8 July with the stated aim of ending rocket attacks and destroying tunnels used by Palestinian militants.
The latest figures from Gaza's health ministry list 1,867 deaths. Some 63 Israeli soldiers and four civilians in Israel have died.
Gaza's Deputy Economy Minister Taysir Amro said the cost could be up to $6bn (£3.55bn).
Separately on Tuesday, Israel revealed it had arrested a Palestinian suspected of involvement in the kidnapping and murder of three Israeli teenagers in June. Hussam Kawasme was arrested on 11 July.
The deaths and subsequent apparent revenge killing of a Palestinian teenager were key factors in escalating tension.