Smoke rises above Gaza after an Israeli air strike on Tuesday along the Gaza-Israel border. As peace talks stall, fighting continues between Hamas and Israeli soldiers, with the Israelis now having entered Gaza City. (Uriel Sinai/Getty Images)

Egypt pressed Hamas to accept a truce proposal Tuesday as the United Nations secretary general left for the Middle East in an effort to boost diplomatic efforts to end the violence.

Ban Ki-moon met with the 15-member UN Security Council before leaving New York for Cairo, where international emissaries have been working to find a diplomatic solution to the violence between Israel and the Palestinian militant group Hamas.

The council passed a resolution last week calling for an immediate end to Hamas rocket attacks and Israeli military action in Gaza. Israeli air strikes started on Dec. 27 after what military officials said was a spike in Hamas rocket attacks.

Ban isn't expected to meet with any Hamas representatives and will not visit Gaza. His stops will include Jordan, Israel, the Palestinian-controlled West Bank, Turkey, Lebanon, Syria and Kuwait.

Hamas negotiators already in Cairo held a new round of talks with Egyptian intelligence officials Tuesday morning. The Egyptian proposal calls for a temporary truce, followed by a long ceasefire and the opening of border crossings with the presence of the Palestinian Authority of President Mahmoud Abbas, whose Fatah party controls the West Bank.

Also Tuesday, Israeli officials said their chief negotiator will travel to Cairo on Thursday. Amos Gilad had put off the trip for days, saying the time was not yet ripe.

Troops push further into city

As diplomatic efforts continued, Israeli troops pushed closer to the densely populated centre of Gaza City. Israeli ground troops battled Palestinian militants in the streets of Tel Hawwa, a neighbourhood of highrise buildings, on Tuesday.

The battles reportedly destroyed dozens of homes, as Israel pushed to less than a kilometre away from Gaza City's crowded centre.

The forces, backed by artillery and attack helicopters, were also moving into neighbourhoods to the east and south of the city as gunboats continued to shell the coast, according to the Associated Press.

Palestinian medical officials reported at least 42 deaths from the conflict on Tuesday throughout Gaza.

Dr. Moaiya Hassanain, a Palestinian health official, said dozens of calls for ambulances had been received, but they could not be dispatched because of the fighting.

The Israeli military said three soldiers were wounded, including an officer who was searching a northern Gaza house when a bomb exploded.

Israelis run for cover in a street bomb shelter during a rocket attack alert in Sderot, neighbouring the Gaza Strip, on Tuesday. Israel continued its ground and air offensive against Gaza for the 18th day. (Yoav Lemmer/AFP/Getty Images)

Some 15 rockets and mortar shells were fired toward Israel Tuesday, but there were no injuries, the Israeli army said.

Israeli aircraft also attacked 60 targets overnight, including tunnels used by Gaza militants to smuggle arms across the border from Egypt.

Despite diplomatic efforts there has been little concrete progress in reconciling key differences between Israel and the militant Palestinian group.

Hamas said on Tuesday it has "substantial reservations" about the Egyptian proposal.

"There are reservations on this initiative, substantial reservations, related to the position of the resistance on the ground," senior Hamas official Moussa Abu Marzouq told Al-Jazeera television.

UN Secretary General Ban Ki-moon, right, addresses a meeting of the Committee on Palestine of Ministers for Foreign Affairs of the Group of Arab States Monday at United Nations headquarters in New York. (Associated Press)

The proposal also calls for international monitors at the borders to prevent smuggling. But Hamas has rejected any international monitors and has demanded a role in controlling the border crossings — which Egypt and Israel rejected.

Since Abu Marzouq's comments, Egyptian President Hosni Mubarak has left on a previously unannounced trip to Riyadh to meet with his ally, Saudi King Abdullah.

Israeli Prime Minister Ehud Olmert said Israel will end military operations only when Hamas stops firing rockets into Israel and halts weapons smuggling across the border. He added that he hopes the efforts in Cairo will "ripen to a result that will enable us to end the fighting."

Israeli defence officials say that depending on what happens in Cairo, Israel will decide whether to move closer to a ceasefire or to launch a new, even tougher stage of its offensive. They spoke on condition of anonymity because they were discussing sensitive policy matters.

Calls for emergency Arab summit

Ban said the focus of his discussions during the trip will be opening border crossings, strengthening border security, providing humanitarian assistance and protecting the civilian population.

Talks will also look at a way to reunite Hamas-controlled Gaza and the Fatah-controlled West Bank, he said.

Before leaving for Egypt, Ban told the Associated Press he has been on the phone constantly with top officials in the Middle East, Europe and the United States promoting a ceasefire. He hopes that direct talks with leaders will have greater influence in coming to a resolution.

"To both sides, I say: 'Just stop, now,' " the UN chief told a news conference Monday. "Too many people have died. There has been too much civilian suffering. Too many people, Israelis and Palestinians, live in daily fear of their lives."

Meanwhile, Qatar has asked the 22-member Arab League in Cairo to hold an emergency Arab summit on Friday.

Two-thirds of the league's 22 members needed to approve the request for the summit to take place. Egypt and Saudi Arabia have rejected the idea, indicating they favour unofficial consultations.

Gaza health officials have reported that more than 940 Palestinians have been killed since the offensive began. Estimates suggest that about 400 of the casualties were women and children and more than 4,000 people have been wounded.

Thirteen Israelis — 10 Israeli soldiers and three civilians hit by mortar bombs and rockets from the Gaza Strip — have been killed.

Israeli Lt.-Gen. Gabi Ashkenazi said Tuesday that troops will continue fighting in Gaza until militant rocket fire has ceased.

"We have achieved a lot in hitting Hamas and its infrastructure, its rule and its armed wing, but there is still work ahead," Ashkenazi told a parliamentary committee on Tuesday.

"We are working to deepen the blow to its military arm, reduce [Hamas] fire, strengthen [Israeli] deterrence and improve the security situation for residents of southern Israel living under the threat of [rocket] attacks," he said.

The fighting has raised concerns of a looming humanitarian disaster in Gaza, where hundreds of thousands of people are without power and running water. The Israeli army said about 100 truckloads of humanitarian aid, including wheat, flour and medical supplies, were to be allowed into the territory on Tuesday.

With files from the Associated Press