A senior Hamas official had told CNN that a "calming down" was to take place, and Egyptian President Mohamed Morsy, who has tried to broker a peace deal, said Tuesday that the "travesty of the Israel aggression on Gaza will end in a few hours."

But after a few hours, Morsy's office told CNN not to expect any announcement.

Prior to Wednesday evening's announcement of a cease-fire, Mousa Abu Marzouk, the deputy leader of Hamas in Cairo, blamed Israel for the breakdown in the talks Tuesday.

"The Israelis did not respond last night at our revised conditions relayed to them through the Egyptian intelligence," he said. "Talk of a temporary cease-fire or 'calming down' was brought to the table, yet they escalated their air strikes late last night as we were trying to reach any sort of cease-fire."

Israeli President Shimon Peres, however, said Hamas was asking for conditions that Israel simply cannot meet.

"They want Israel to do nothing. We shall not fly over, we shall not guard the border," he told CNN's Wolf Blitzer. "Many others. The conditions of Israel is basically security conditions. Their conditions are political ones and this is a contradiction."

The IDF said it had targeted "dozens of terror infrastructure sites," overnight, including Hamas' Ministry of Internal Security, which it saw as a "main command and control center."

Forces also took aim at a police compound, a "military hideout," and other targets it linked to what it called Hamas' "terror activity."

The Israeli military also struck a media building, where it said Hamas "deliberately located" an "intelligence operation center," and a system of tunnels used to transport fuel.

Militants lobbed rockets and missiles toward Israel, targeting military bases, radar sites and numerous cities, including Beer Sheva, according to the al Qassam Brigades' Twitter feed.

A rocket alarm howled in the Israeli city of Ashkelon shortly after 7:30 a.m. Wednesday, just minutes after Hamas' TV broadcaster al-Aqsa reported its militants' rockets striking there as well as in the towns of Sderot and Ashdod. CNN's Fred Pleitgen in Ashkelon heard two impacts but could not yet say if the rockets hit anything.

All told, militants had fired 62 rockets from Gaza as of Wednesday afternoon, with 42 landing in Israel, according to the IDF. The Israeli military's Iron Dome defense system intercepted the other 20, the IDF said.

Diplomats working on a cease-fire hope to avoid a repeat of 2008 and 2009, when at least 1,400 people died when Israeli troops invaded Gaza after a similar spate of rocket attacks.

At least 142 people have died in Gaza since the Israeli airstrikes began, according to the Ministry of the Interior in Gaza. Another 1,180 have been injured, the ministry said. In Israel, five people have died and 94 have been wounded, according to authorities.

Clinton shuttled between meetings with Palestinian and Israeli leadership Wednesday, then moved on to Cairo, where she met with Morsy Wednesday night.

She met earlier in the day with Palestinian Authority President Mahmoud Abbas in Ramallah in the West Bank, according to the U.S. Embassy, as well as with Israeli Prime Minister Benjamin Netanyahu in Jerusalem for a second day.

Abbas told Clinton that Gaza is facing a humanitarian crisis and that an immediate cease-fire is needed, according to the official Palestinian news agency WAFA.

Clinton is not expected to travel to Gaza, which is run by Hamas, considered a terrorist organization by the United States and other countries.

Ban also met with Abbas in Ramallah Wednesday morning.

"Today the situation in Gaza is deeply alarming," Ban said, standing next to Abbas at a news conference. "Rockets aimed at military targets inside Gaza are killing and injuring civilians and damaging... civilian infrastructures."

He demanded that diplomacy pave the way forward and called for the emergence of a Palestinian state.

Pope Benedict, speaking from Vatican City, also issued a plea for peace.

"I feel the duty to reiterate once again that hatred and violence are not the solution to problems," he said.