Nevertheless, Palestinian rocket fire and Israeli air strikes continued for a seventh day.
Hamas militants said they fired 16 missiles at the southern Israeli city of Beersheba after Israel's military targeted roughly 100 sites in Gaza overnight, including ammunition stores and the Gaza headquarters of the National Islamic Bank.
Some 110 Palestinians have died in a week of fighting, the majority of them civilians, including 27 children. Three Israelis died last week when a Gaza missile struck their house.
Ban Ki-moon called for an immediate ceasefire and said a ground operation by Israel in Gaza would be a "dangerous escalation" that must be avoided.
He had held talks in the Egyptian capital with Arab League chief Nabil Elaraby and was due to meet Egypt's Islamist President Mohamed Mursi before travelling to Israel for talks with the country's Prime Minister Benjamin Netanyahu.
Israel's leaders weighed the benefits and risks of sending tanks and infantry into the densely populated coastal enclave two months before an Israeli election, and indicated they would prefer a diplomatic path backed by world powers, including US President Barack Obama, the European Union and Russia.
The White House said US Secretary of State Hillary Clinton was going to the Middle East for talks in Jerusalem, Ramallah and Cairo to try to calm the conflict. An source in Israel said she was expected to meet Netanyahu on Wednesday.
Netanyahu and his top ministers debated their next moves in a meeting that lasted into the early hours of Tuesday.
"Before deciding on a ground invasion, the prime minister intends to exhaust the diplomatic move in order to see if a long-term ceasefire can be achieved," a senior Israeli official, speaking on condition of anonymity, said after the meeting.
Palestinians should be 'equipped'
Iran says Palestinians in the Gaza Strip should be "equipped" to defend themselves against Israel.
But Foreign Ministry spokesperson Ramin Mehmanparast refused to comment on Israel's allegations that Iran is already sending arms to Gaza, which has been under Israel's attack since last week in retaliation for rockets fired by Hamas into Israel.
At least 113 Palestinians have been killed – nearly half of them civilians.
Iran is a major supporter of the militant groups such as Islamic Jihad and Hamas, which controls Gaza.
Mehmanparast also said on Tuesday that Israel should be put on trial for war crimes over the latest offensive.
Iran has previously denied it had directly supplied Hamas with Iran-made Fajr-5 missiles that have hit near Tel Aviv and Jerusalem.
A delegation of nine Arab ministers, led by Egypt's foreign minister, were due in Gaza later on Tuesday in a further signal of heightened Arab solidarity with the Palestinians.
Any diplomatic solution may pass through Egypt, Gaza's other neighbour and the biggest Arab nation, where the ousting of US ally Hosni Mubarak and the election of Mursi is part of a dramatic reshaping of the Middle East wrought by Arab uprisings and now affecting the Israel-Palestine conflict.
Mursi, whose Muslim Brotherhood was mentor to the founders of Hamas, took a call from Obama on Monday telling him the group must stop rocket fire into Israel – effectively endorsing Israel's stated aim in launching the offensive last week. Obama, as quoted by the White House, also said he regretted civilian deaths – which have been predominantly among the Palestinians.
"The two leaders discussed ways to de-escalate the situation in Gaza, and US President Barack Obama underscored the necessity of Hamas ending rocket fire into Israel," the White House said, adding that the US leader had also called Netanyahu.
"In both calls, President Obama expressed regret for the loss of Israeli and Palestinian civilian lives."
Egypt sees deal
Mursi has warned Netanyahu of serious consequences from a ground invasion of the kind that killed more than 1 400 people in Gaza four years ago. But he has been careful not to alienate Israel, with whom Egypt's former military rulers signed a peace treaty in 1979, or Washington, a major aid donor to Egypt.
Egypt's Prime Minister Hisham Kandil told Reuters a ceasefire was possible: "I think we are close, but the nature of this kind of negotiation, (means) it is very difficult to predict."
After Hamas leader Khaled Meshaal laid out demands in Cairo that Israel take the first step in restoring calm, and warned Netanyahu that a ground war in Gaza could wreck his re-election prospects in January, a senior official from Israel denied a Hamas assertion that the prime minister had asked for a truce.
"Whoever started the war must end it," Meshaal said, referring to Israel's assassination from the air on Wednesday of Hamas's Gaza military chief, a move that followed a scaling up of rocket fire onto Israeli towns over several weeks.
An official close to Netanyahu told Reuters: "We would prefer to see a diplomatic solution that would guarantee the peace for Israel's population in the south. If that is possible, then a ground operation would no longer be required."
Fortified by the ascendancy of fellow Islamists in Egypt and elsewhere, and courted by fellow Sunni Arab leaders in the Gulf keen to draw the Palestinian group away from old ties to Shi'ite Iran, Hamas has tested its room for manoeuvre, as well as longer-range rockets that have reached the Tel Aviv metropolis.
Israel's statistics showed some easing in the ferocity of the exchanges on Monday. Israel's police counted 110 rockets, causing no casualties, of which 42 were shot down by anti-missile batteries. Tuesday's salvo also caused no injuries.
There has been no attack on Tel Aviv since Sunday.
Hamas said four-year-old twin boys had died with their parents when their house in the town of Beit Lahiya was struck from the air during the night. Neighbours said the occupants were not involved with militant groups.
Israel had no immediate comment on that attack. It says it takes extreme care to avoid civilians and accuses Hamas and other militant groups of deliberately placing Gaza's 1.7-million people in harm's way by placing rocket launchers among them.
Nonetheless, fighting Israel, whose right to exist Hamas refuses to recognise, is popular with many Palestinians and has kept the movement competitive with the secular Fatah movement of Palestine's President Mahmoud Abbas, who remains in the West Bank after losing Gaza to Hamas in a civil war five years ago.
"Hamas and the others, they're our sons and our brothers, we're fingers on the same hand," said 55-year-old Faraj al-Sawafir, whose home was blasted by Israeli forces. "They fight for us and are martyred, they take losses and we sacrifice too."
In scenes recalling Israel's 2008/09 winter invasion of the coastal enclave, tanks, artillery and infantry have massed in field encampments along the sandy, fenced-off border.
Israel has also authorised the call-up of 75 000 military reservists, so far mobilising around half that number.
Although 84% of Israelis support the current Gaza assault, according to a poll by Israel's Haaretz newspaper, only 30% want an invasion.
In an echo of frictions over the civil war in Syria, Russia accused the United States on Monday of blocking a bid by the UN Security Council to condemn the escalating conflict in the Gaza Strip. Washington has generally stopped the UN body from putting what it sees as undue pressure on its ally, Israel. – Reuters, AP