An Israeli envoy has arrived in Egypt for possible negotiations on a ceasefire as the barrage on Gaza intensified and the prime minister, Binyamin Netanyahu, threatened to "significantly expand" military operations.

Amid signs of Israeli preparations for an invasion, the US and UK signalled that although they accepted that strikes against Gaza had been justified because of rockets fired by militants inside the Palestinian enclave, their support would lessen if Israel sent in troops and tanks.

"Israel has every right to expect that it does not have missiles fired into its territory," Barack Obama said at the start of a three-nation tour in Asia. "Let's understand what the precipitating event here was … that was an ever escalating number of missiles that were landing not just in Israeli territory but in areas that are populated.

"There is no country on earth that would tolerate missiles raining down on its citizens from outside its borders." The US president said it would be preferable if the Israeli operation against rocket launchers in Gaza could be accomplished without "a ramping-up of military activity".

Obama added: "It's not just preferable for the people of Gaza. It's also preferable for Israelis, because if Israeli troops are in Gaza, they're much more at risk of incurring fatalities or being wounded."

Britain's foreign secretary, William Hague, told Sky News that the ruling Hamas party bore "principal responsibility" for the current conflict, but added that a ground invasion would "lose Israel a lot of the international support and sympathy they have in this situation".

A senior Israeli official in Jerusalem confirmed to the Haaretz newspaper that an envoy had been dispatched to Cairo for ceasefire talks. The envoy was not named and the official said Israel did not expect a breakthrough and preparations for a possible ground offensive were continuing.

Reports from Cairo said the unnamed envoy had been taken straight from the airport to secret talks with Egyptian officials. Nabil Shaath, an aide to the Palestinian president, Mahmoud Abbas, who was also in Cairo, described the contacts between Israel and Egypt as "serious attempts to reach a ceasefire".

The Hamas prime minister, Ismail Haniyeh, was reported to have spoken to the Egyptian president, Mohamed Morsi, and told him he supports such talks, provided Hamas received "guarantees that will prevent any future aggression" by Israel, according to a statement issued from Haniyeh's office.

Netanyahu was reported to have told Obama and the German chancellor, Angela Merkel, that Israel might agree to a ceasefire if all rocket fire ceased from Palestinian territory.

In southern Israel, contingents of reservists who had been called up in anticipation of a possible ground operation in Gaza arrived near the border on Sunday, and military vehicles trundled along nearby roads, some of which have been closed to civilian traffic.

Hamas's repeated targeting of Tel Aviv, Israel's densely populated cultural and commercial centre, raised expectations that Netanyahu would respond to pressure to step up action to halt rocket fire from Gaza.

However, both sides are thought to be keen to avoid such an escalation. "No matter what Hamas's capabilities are, they will not be able to defend Gaza from Israel [in the event of a ground offensive]," said Mkhaimer Abu Saada, a political scientist at Gaza's al-Azhar university.

Israel, despite its hawkish rhetoric, is also aware that the high casualties that are inevitable in a ground offensive are likely to result in a sharp change of tone from the international community.

Abu Saada said there were two likely scenarios: a limited ground operation with Israeli troops and tanks entering and occupying relatively small areas of Gaza and withdrawing as soon as possible, as happened in Operation Cast Lead, the 22-day offensive in 2008-9; or a much bigger operation to "hit Hamas hard, weakening it to the point where it was no longer capable of ruling Gaza".

However, to prevent even more extremist militant organisations filling the resulting power vacuum, Israel would have to reoccupy Gaza on a long-term basis. "This is probably the last thing in Israel's mind," he said.

"Netanyahu is in a dilemma now," Abu Saada said. Now that he has started the war, it is not clear how to end it in a way that would meet Israel's goal of restoring deterrence and punishing Hamas without becoming embroiled in a full-scale military occupation.

The Israel Defence Force said it attacked 50 targets on Sunday, including Hamas rocket launchers. The BBC reported that seven Hamas officials' homes had also been hit. The IDF said 900 rockets had been fired from Palestinian territory into Israel over the five days of fighting, of which 302 had been hit by Israeli interceptors fired by Israel's Iron Dome anti-missile system. Eight Israelis were reported wounded in rocket strikes on Sunday.

According to Israeli officials, more than 100 rockets fired from Gaza have fallen within the Palestinian enclave, some causing injuries and deaths.

The Palestinian Centre for Human Rights said an investigation suggested the deaths of a four-year-old child and a 22-year-old man in Jabaliya, north of Gaza City, on Friday had been caused by a rocket that had fallen short of its target.