President Obama and Secretary of State Hillary Clinton arrive in Burma, Nov. 19, 2012. / Getty
Updated at 8:05 a.m. Eastern
PHNOM PENH, Cambodia President Obama is sending Secretary of State Hillary Rodham Clinton to the Middle East in hopes that she can help mediate an end to the bloody conflict between Israel and Gaza, even as a second rocket landed close to Jerusalem on Tuesday.
A deputy White House national security adviser told CBS News that Clinton would depart Tuesday from Cambodia, where she had accompanied Mr. Obama on a visit to Southeast Asia.
Clinton was to begin her Mideast diplomacy by meeting Israeli Prime Minister Benjamin Netanyahu in Jerusalem. She was then to meet Palestinian officials in Ramallah before heading to Cairo to meet Egyptian leaders. Mohammed Morsi, a Muslim Brotherhood politician with ties to Hamas, was elected president of Egypt earlier this year and has taken a lead role in trying to negotiate a ceasefire between Israel and the Gaza militants.
Even as talk of a possible two-phase cease-fire deal gained steam, however, a Palestinian rocket struck the outskirts of Jerusalem, landing harmlessly in an open area in one of the longest rocket strikes fired from the Gaza Strip in nearly a week of fighting.
The rocket attack, the second aimed at the holy city since an Israeli offensive began a week ago, set off air raid sirens throughout the metropolis. A distant explosion could be heard in the city's downtown and Jerusalem residents ran for cover as buses and trains stopped to let passengers off.
Police spokesman Micky Rosenfeld said the rocket landed in Gush Etzion, a collection of Jewish West Bank settlements southeast of the city. Last Friday's attempt to hit Jerusalem landed in the same area. No one was wounded in either attack.
CBS News White House correspondent Bill Plante reports that Clinton will meet officials from the Palestinian Authority, based in the West Bank, while she's in Israel, but she won't deal directly with Hamas. She will instead press Egypt to use its leverage with the Islamic militants to get a deal agreed to, and Plante says both the White House and the Egyptians are very aware of increasing pressure in the U.S. Congress to cut the more than $1 billion in military aid Washington gives to Egypt.
In the latest sign that the intensive diplomacy might be paying off, a source close to the Hamas delegation in Cairo told CBS News correspondent Clarissa Ward on Tuesday morning that he believed some agreement would be reached "within a few hours." He said the negotiating parties were still trying to work out the logistics of implementing a ceasefire on the ground.
According to the source, Israel wants Hamas to stop rocket fire for an initial 24 hours, and then the Jewish state would theoretically meet some of the militant group's demands. Ward notes, however, that previous remarks from diplomats suggesting a deal was near have proven premature, as Israel remains reluctant to accept Hamas' key demand that a total blockade on the Gaza Strip be lifted. Israel fears that lifting the blockade would allow more weapons to flow into the tiny Palestinian territory.
There was no immediate comment from Israel on the progress of the negotiations.
A State Department official told CBS News that Clinton's visit was intended to, "build on American engagement with regional leaders over the past days - including intensive engagement by President Obama with Prime Minister Netanyahu and President Morsi - to support de-escalation of violence and a durable outcome that ends the rocket attacks on Israeli cities and towns and restores a broader calm."
The official added praise for the role Morsi has taken in the talks and said the Obama administration was "hopeful that these efforts will be successful."
Efforts to negotiate an end to a week-old convulsion of the latest Israeli-Palestinian violence also brought the U.N. chief to the region on an emergency mission.
Israeli aircraft Tuesday battered the headquarters of the bank Hamas set up to sidestep international sanctions on its rule.
The strike on the Islamic National Bank was part of a widening Israeli assault against Gaza militants meant to quell rocket fire that has struck deep into Israel's heartland. U.N. chief Ban Ki-moon's itinerary was taking him Tuesday to Egypt and Israel, where he hoped to prod the two sides to reach a deal.
From Cairo, Ki-moon said he came because of the "alarming situation" in the region.
"This must stop, immediate steps are needed to avoid further escalation, including a ground operation," Ban said. "Both sides must hold fire immediately. ... Further escalation of the situation could put the entire region at risk."
Israel and Gaza's militant Hamas rulers have staked tough, hard-to-bridge positions, and the gaps keep alive the threat of an Israeli ground invasion. In the meantime, grieving Gazans buried militants and civilians killed in ongoing Israeli airstrikes, and barrages of rockets from Gaza sent terrified Israelis scurrying to take cover.
The conflict erupted last week, when a resurgence in rocket fire from Gaza provoked Israeli Prime Minister Benjamin Netanyahu's government to strike back, killing Hamas' military chief in an air attack and carrying out hundreds of assaults on militants' underground rocket launchers and weapons stores.
The onslaught abruptly turned deadlier over the weekend as aircraft were ordered to go after Hamas military commanders and buildings suspected of housing their commands and weapons caches. In the narrow warrens of crowded Gaza, where militants often operate from residential areas, civilian casualties mounted.
By Tuesday, civilians accounted for 54 of the 113 Palestinians killed since the operation began. Some 840 people have been wounded, including 225 children, Gaza health officials said.
Tuesday's attack on the Islamic National Bank in Gaza was the latest in a string of assaults on Hamas symbols of power. Leading Hamas members set up the bank after it violently overran Gaza in June 2007 because foreign lenders, afraid of running afoul of international terror financing laws, stopped doing business with the militant-led Gaza government.
Israel, the U.S. and other Western powers consider Hamas, which has killed hundreds of Israelis in suicide bombings and other attacks, a terror group.
The inside of the bank, which describes itself as a private enterprise, was destroyed. A building supply business in the basement was damaged.
Fuad Hijazi and two of his toddler sons were killed Monday evening when missiles struck their one-story shack in northern Gaza, leaving a crater about 7- to 10-feet deep in the densely populated neighborhood. Residents said he was not a militant.
On Tuesday morning, the boys' bodies lay next to each other on a rack in the local morgue, wrapped tightly in white burial shrouds. Their father lay in a rack below.
"We want to tell the world which is supporting the state of Israel, what this state is doing," said neighbor Rushdie Nasser. "They are supporting a state that kills children. ... We want to send a message to the U.N. and the West: Enough of supporting the Zionists, who are killing children."
Three Israeli civilians have also been killed and dozens wounded since the fighting began last week, the numbers possibly kept down by a rocket-defense system known as Iron Dome that Israel developed with U.S. funding. More than 1,000 rockets have been fired at Israel this week, the military said, including three that struck schools that had been emptied because of the fighting.
CBS News correspondent Allen Pizzey reports the barrage of missiles from Gaza into southern Israel tapered off significantly on Monday, but one managed to evade the Iron Dome system and slam into the town of Be'er Sheva. Parked vehicles were destroyed, but there were no casualties.