US Secretary of State John Kerry held discussions in neighbouring Egypt, while UN Secretary General Ban Ki-moon met Prime Minister Benjamin Netanyahu in Tel Aviv and planned to see the Palestinian prime minister in the occupied West Bank today.
However, there was no let-up in the fighting around Gaza, with plumes of black smoke spiralling into the sky and Israeli shells raining down on the coastal Palestinian enclave.
Hamas and its allies fired more rockets into Israel, triggering sirens in Tel Aviv. One hit a town on the fringes of Ben-Gurion International Airport, slightly injuring two people.
Justice Minister Tzipi Livni, viewed as the most dovish member of Netanyahu's inner security cabinet, said: "A ceasefire is not near. I see no light at the end of the tunnel."
Mr Kerry said after talks with Egyptian Foreign Minister Sameh Shukri: "There is a framework to end the violence and that framework is the Egyptian initiative.
"For the sake of thousands of innocent families whose lives have been shaken and destroyed by this conflict, on all sides, we hope we can get there as soon as possible."
Egypt was key to securing an end to a previous bout of Gaza fighting in 2012, but the country's new leadership is openly hostile to Hamas, possibly complicating the negotiations.
With the conflict entering its third week, the Palestinian death toll rose to 613, including nearly 100 children and many other civilians.
Israel's casualties also mounted, with the military announcing the deaths of two more soldiers, bringing the number of army fatalities to 27 - almost three times as many as were killed in the last ground invasion of Gaza, in a 2008-2009 war.
Two Israeli civilians have also been killed by Palestinian rocket fire into Israel.
With Mr Netanyahu at his side, Mr Ban said: "My message to Israelis and Palestinians is the same: Stop fighting. Start talking. And take on the root causes of the conflict, so we are not back to the same situation in another six months or a year."
An Egyptian official who attended some of Mr Kerry's meetings said Mr Ban was working toward reaching a humanitarian truce, perhaps lasting for several days, to get aid into the territory.
With Israeli shells and bombs hitting Gaza day and night, thousands of people have fled districts close to the border. The main UN agency in Gaza, UNWRA, said almost 102,000 people had taken shelter in 69 of its schools.
Jens Laerke, of the UN Office for the Coordination of Humanitarian Affairs (OCHA), said: "There is literally no safe place for civilians."
Israel has signalled it is in no hurry to achieve a truce before reaching its goal of crippling Hamas's militant infrastructure, including rocket arsenals and networks of tunnels threatening Israelis living along the Gaza frontier.
Hamas has said it will not cease hostilities until its demands are met, including that Israel and Egypt lift their blockade of Gaza and its 1.8 million people, and that Israel release several hundred Palestinians detained during a search last month for three Jewish teenagers later found dead.
Israel blamed the killings on Hamas, and their deaths, along with the revenge slaying of a Palestinian teen, were factors in a flare-up of violence along the Israel-Gaza border last month that escalated into the current fighting.
In Israel, the military said it had identified the remains of six soldiers killed in an attack on their armoured vehicle in Gaza on Sunday and was trying to identify the seventh.
Prompting widespread celebrations in Gaza, Hamas's armed wing announced on Sunday it had captured a soldier. It displayed a photo ID and army serial number of the man, but did not show any image of him in their hands.
The Israeli military believes it was impossible for anyone to have survived the direct hit on the armoured vehicle in which the missing man was travelling.
Israel has agreed to mass releases of Palestinian prisoners in the past to secure the freedom of captured soldiers, or even for the return of the bodies of its citizens.