US Secretary of State John Kerry made the appeal after meeting Egyptian president Abdel Fattah al-Sisi. Egypt has previously acted as mediator in the Arab-Israeli conflict.
Mr Kerry was upbeat about the talks, but warned there was still “work to do” to try to resolve a renewed conflict in which more than 600 have died.
“Hamas has a fundamental choice to make and it is a choice that will have a profound impact for the people of Gaza,” Mr Kerry told reporters in a joint appearance with his Egyptian counterpart Sameh Shukri.
“The Egyptians have provided a framework and a forum for them to be able to come to the table to have a serious discussion together with other factions of the Palestinians.”
Hamas has already rejected the Egyptian initiative, saying the plan ignores its demands for the release of prisoners and for a more comprehensive lifting of an economic blockade on the Gaza Strip.
Egypt is deeply suspicious of Hamas because it is an offshoot of the Muslim Brotherhood, the Islamist movement toppled by then army chief Gen Sisi last year. Hamas has complained Cairo froze it out of talks on the ceasefire proposal. Officials in Cairo say they have consulted all Palestinian factions.
Mr Kerry, who earlier in the day met separately with Mr Shukri and with Arab League chief Nabil al-Araby, stressed that after any ceasefire was achieved the parties would need to grapple with the underlying issues in their conflict.
“Just reaching a ceasefire, clearly, is not enough,” he said. “It is imperative there be a serious engagement, discussion, negotiation, regarding the underlying issues and addressing all of the concerns that have brought us to where we are today.”
Mr Kerry also said the US was sending $47 million (£28m) in aid to Gaza “to alleviate the immediate humanitarian crisis”. He is expected to stay in Cairo for talks with Egyptian officials and the Arab League chief Mr Araby.
United Nations Secretary-General Ban Ki-moon yesterday also urged Israel and the Palestinians to “stop fighting” and “start talking” to end the conflict.
He was speaking in Israel as diplomatic efforts intensified.
More than 600 Palestinians and 30 Israelis have been killed in the past 14 days of fighting, officials say.
At a joint news conference with Israeli prime minister Benjamin Netanyahu, Mr Ban urged Israel to exercise “maximum restraint”, adding that “military action will not increase Israeli security in the longer term”. He called on the Palestinians to pursue a policy of “no violence, recognition of Israel and respect for previous agreements”.
Replying to Mr Ban’s opening comments, Mr Netanyahu asked: “What grievance can we resolve for Hamas?
“Their grievance is that we exist.”
The latest Palestinian death toll of more than 600 was announced by Gaza’s health ministry, which also said that 3,640 people had been injured.
The UN relief agency in Gaza said one of its schools, in which around 300 people had been taking shelter, had been hit by Israeli shelling yesterday.
It said more than 118,300 Palestinians have now taken refuge in its shelters. It says 43 per cent of Gaza has been affected by evacuation warnings or declared no-go zones.
The majority of Palestinians killed have been civilians, including dozens of children, according to the UN.
The Israel Defence Force also says it has killed at least 170 militants. Israel says 28 of its soldiers and two Israeli civilians have died over the past two weeks.