Israel and Gaza are under international pressure to agree on a ceasefire, after six days of air strikes and rocket attacks which have killed 110 Palestinians and three Israelis.
As Israel launched 100 air strikes overnight, and 37 rockets were fired into southern Israel, diplomats are meeting in Egypt to agree plans to halt fire.
Ban Ki-Moon, the UN's secretary general, and Hillary Clinton are both due to visit Israel on Tuesday to advance the efforts. Clinton will not meet Hamas officials.
According to Israel's Haaretz newspaper, Hamas' Khaled Meshal and Islamic Jihad's Ramadan Abdullah Shalah will meet Egypt's Raafat Shehata to agree a ceasefire.
The BBC reports that Israel has put plans for a ground operation in Gaza "on hold" to allow ceasefire talks a chance.
British Foreign Secretary William Hague will make a statement to MPs on Tuesday about the Gaza conflict. On Monday the foreign secretary paid tribute to Egyptian efforts to negotiate "a ceasefire that can work".
He praised Egyptian ceasefire negotiators for averting an Israeli ground invasion so far in the crisis and said the fact that Israel was holding back from an invasion of Gaza, and that rocket attacks on Israel were lessening, were "positives" in an otherwise desperate situation.
Foreign Office minister Alistair Burt arrived in Israel yesterday for a three-day visit, during which he will also go to the Gaza Strip.
He will meet senior Israeli ministers and Palestinian president Mahmoud Abbas and prime minister Salam Fayyad.
On Tuesday he visited Kiryat Malachi where a rocket hit a residential building, killing three Israeli civilians last week.
"I am gravely concerned about the current crisis, particularly the loss of civilian life on both sides," he said.
Speaking at a news conference in Cairo on Monday, Khaled Meshaal, exiled leader of Hamas, said a truce was possible but Israel must halt its strikes first and lift its blockade of Gaza.
He added that Netanyahu was concerned about the impact of a "land war" domestically because of elections in January.