United States Secretary of State John Kerry urged Hamas on Tuesday to pursue a negotiated end to its conflict with Israel after what he said were constructive talks with Egyptian officials about their ceasefire proposal, according to The Associated press.

After meeting Egyptian President Abdel Fattah al-Sisi, whose country has some leverage over Hamas through its control of a border crossing from Egypt to the Gaza Strip, Kerry said there was still "work to do" to resolve the conflict, the AP reported.

Israel pounded targets in the Gaza Strip on Tuesday and Justice Minister Tzipi Livni, seen as the most dovish member of Prime Minister Benjamin Netanyahu's inner security cabinet, told Israeli Army Radio: "A ceasefire is not near," according to the AP.

More than 600 people have died since Israel launched an offensive on July 8 to halt missile attacks out of the Gaza Strip by Hamas, which has been angered by a crackdown on its supporters in the occupied West Bank and by its suffering economic hardship because of an Israeli-Egyptian blockade, the AP reported.

"Hamas has a fundamental choice to make and it is a choice that will have a profound impact for the people of Gaza," Kerry told reporters in a joint appearance with his Egyptian counterpart, Sameh Shukri, according to the AP.

Kerry said his discussions with Shukri sought to "hopefully find not only a way to a cease-fire, but a way to deal with the underlying issues, which are very complicated," the AP reported. Kerry stopped short of agreeing to reopen the peace talks that abruptly broke off last April after nearly nine months of his personal attention.

"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," Kerry added, calling the U.S.-Egyptian talks "constructive meetings," according to the AP.